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In this thesis, the results of torque magnetometry and electronic transport studies of the archetypal cuprate superconductor YBa₂Cu₂O₆₊ₓ (YBCO) are presented. By variation of temperature, doping or application of a magnetic field, it is possible to access several underlying electronic phases that occur on the backdrop of superconductivity. Of particular interest in this thesis are the pseudogap, an elusive phase possibly tied to a quantum critical point at p » 0.19 within the superconducting dome, and charge density wave (CDW) order, which seems ubiquitous in the cuprates and appears to be competing with superconductivity. Firstly, magnetic torque measurements at 14 T in the underdoped region of the phase diagram (p= 0.08 - 0.15) are presented. Magnetic torque is used to investigate the nature of the pseudogap transition, believed to be a second order nematic phase transition, and determine whether the transition temperature T* marks the boundaries of a thermodynamic phase. The in-plane magnetic susceptibility anisotropy feature observed does not track the pseudogap onset, it is the result of a doping dependent linear contribution and a p-independent contribution, either coming from the experimental setup or the orthorhombicity of the crystal. Secondly, resistivity and Hall effect measurements at 14 T in disordered YBCO (p »0.125) are presented. Point-like disorder, either by chemical substitution of Zn and Ni inside the material or by electron irradiation, is introduced in YBCO to gradually suppress superconductivity. The evolution of the superconducting transition temperature Tc and the temperature at which the Hall coefficient changes sign T₀, an indicator of a Fermi surface reconstruction due to the onset of charge order, are tracked as a function of point-like disorder. Tc is used as a measure of the strength of superconductivity whilst T0 is used as a proxy for the strength of charge order. Both Tc and T₀ are shown to decrease as a function of disorder, in contrast with X-ray measurements where CDW seem to be weakly affected by disorder and in competition with superconductivity. The implications with regard to this discrepancy are discussed. Thirdly, resistivity and Hall effect measurements at 14 T in YBCO (p »0.13) under uniaxial pressure are presented. Two uniaxial pressure devices, newly designed for high magnetic field, are used to apply strain to YBCO crystals. The evolution of Tc and T₀ are tracked as a function of strain. The devices proved to be able to effectively change the superconducting critical temperature and affect T₀ with the same success rate as a commercially available setup unsuited for high field measurements, making these results a promising proof of concept for future uniaxial pressure research at high magnetic fields.

The isolation of graphene in 2004 started a new development in the field of condensed matter physics and materials science to use graphene's impressive electronic properties and mechanical versatility to improve upon existing electrical devices. One of several types of key devices that graphene could become incorporated into is the Hall-effect magnetic field sensor. Within this project CVD graphene Hall probes with wire widths from 1.5mu m down to 50nm have been fabricated and characterised to explore the possibility of replacing III-V semiconductor-based 2D electron gas Hall probes that are the current standard in scanning Hall probe microscopy. The minimum detectable field of the graphene Hall probes was estimated by measuring their Hall coefficients, and characterising the low frequency electronic noise between 1Hz and 1kHz using a dynamic spectrum analyser. The minimum detectable field was mapped as a function of wire width, carrier density and current density. This revealed that it can be optimised by increasing the current density, with performance improvements being particularly pronounced in devices with micrometer-scale dimensions. The minimum detectable field can also be tuned by back gating the devices on a Si/SiO2 substrate, allowing the carrier density and type to be controlled. In this way, the minimum detectable field can be substantially improved by reducing the carrier density close to the charge neutrality point. In practice its dependence on the wire width is surprisingly weak. However, a large increase in the minimum detectable field is seen when the width drops below 85nm, associated with a drop in mobility as edge roughness-induced charge scattering begins to dominate. To improve the minimum detectable field, graphene devices passivated by HSQ and encapsulated in exfoliated hBN flakes have been fabricated and characterised. Passivation by HSQ yields a small improvement in the electrical mobility as estimated from Hall measurements, while the biggest improvements are found by encapsulation with hBN. This improvement in mobility substantially improves the minimum detectable fields, with encapsulated devices exhibiting an order of magnitude better detection limit than unencapsulated CVD graphene. Resistance versus back gate voltage measurements on devices encapsulated with hBN also show significantly lower extrinsic doping levels than unencapsulated devices, thus removing the need to gate such devices to achieve optimal carrier densities near the CNP. These encouraging results reveal that encapsulated graphene is a promising material for the sensors of the next generation of high resolution scanning Hall probe microscopes. Scanning Hall probe microscopy with a GaAs/AlGaAs 2D electron gas-based Hall probe has been used to explore the unique interplay between superconductivity and ferromagnetism in the Fe-based material, RbEuFe4As4. Quantitative magnetic images of superconducting vortices allows the direct extraction of the superconducting penetration depth from the vortex profiles as a function of temperature. This reveals a pronounced increase in the penetration depth near the magnetic transition temperature, in good agreement with a recently developed model describing the change in superfluid density as a result of the ordering of the magnetic moments. This shows that there is a significant interplay between the two types of order within the material, yet the exchange interaction between superconducting and magnetic sublattices is still weak enough that both are able to coexist. Scanning Hall probe microscopy has also been used to characterise the vortex pinning landscape in second generation GdBaCuO high temperature superconducting tapes. Local Hall probe magnetometry was employed to estimate the critical current, while topographic and magnetic imaging reveals that the films contain strong distinct vortex pinning sites. Comparing magnetic and topographic images reveals that these are most likely linked to the GdO second phases formed during thin film growth, as opposed to grain boundaries and normal CuO phases that protruding from the surface of the superconducting layer. This suggests that the engineering of high critical current tapes should focus on optimising the film microstructure and pinning sites during growth, rather than the addition of extra artificial pinning post-growth sites.

Measuring electron temperature is an important method to understand the stability and coherence of a quantum circuit, since this variable describes how `quiet' the electronic environment is. In this thesis, the construction, calibration and operation of a quantum dot electron thermometer is demonstrated in two different cryostats. Compared to previous implementations of a quantum dot thermometer, the work presented here is unique in that it only requires a single gate connection to calibrate and operate, which simplifies the application of the device substantially. For the thermometer calibration, a physical model of the quantum-dot reservoir system was developed, which reveals information usually obtained from a stability diagram. Electron thermometry was successfully performed with the calibrated thermometer in a 1.0 K to 3.0 K range. With the fastest mode of operation the quantum dot thermometer was shown to have a sensitivity of 3.7±0.3 mK/√Hz at 1.3 K. This device provides a new versatile, sensitive and effective tool for monitoring electron temperature in nanoelectronic devices at cryogenic temperatures. Also in this thesis, several plastic solid-void structures were demonstrated to offer excellent thermal and structural properties at sub-Kelvin temperatures. Good low temperature insulators are extremely useful for support cryogenic components and sample environments without leaking unwanted heat. A structure fabricated from commercially available ABS LEGO elements was shown to be effective at thermally insulating two bodies at sub-Kelvin temperatures, with a thermal conductivity of κ = (8.7±0.3)×10-5 T1.75±0.02 Wm-1K-1. Similar scale 3D printed ABS and PLA gyroid structures were shown to also be effective as low-temperature insulators, having a thermal conductivity of κ = (3.07±0.05)×10-5T1.72±0.02 Wm-1K-1 and κ = 4.45±0.05)×10-5T1.64±0.02 Wm-1K-1, respectively. These samples demonstrate how low temperature insulation can be improved with readily available, fully customisable and affordable components.

I n this work we have implemented the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn-Rostoker (KKR) method for solving, self-consistently, the spin-polarised superconducting state for 3d crystals including substitutional impurities. The generalisation to the fully relativistic Dirac-Bogoliubov-de Gennes (DBdG) equations is also implemented for 3d crystals. This method combines the full complexity of the underlying electronic structure and Fermi surface geometry with a simple phenomenological parametrisation for the superconductivity. We apply this theoretical framework to the known s-wave superconductors Nb, Pb, and MgB2. In these materials multiple distinct peaks at the gap in the density of states were observed, showing significant gap anisotropy which is in good agreement with experiment. For Pb the effects of spin-orbit coupling and the surface gap anisotropy are also addressed. Qualitatively, the results can be explained in terms of the k-dependent Fermi velocities on the Fermi surface sheets exploiting concepts from Bardeen-Cooper-Schrieffer (BCS) theory. We then investigate how impurities affect the superconducting state by applying the theoretical framework to bulk Nb with non-magnetic impurities. Without non-magnetic impurities, Nb has an anisotropic gap structure with two distinct peaks around the Fermi level. In the presence of non-magnetic impurities those peaks are broadened due to the scattering between the two bulk superconducting gaps, however the peaks remain separated. As a second example of self-consistent real-space solutions of the BdG equations we examine superconducting clusters embedded within a non-superconducting bulk metallic host. This allows us to estimate the coherence length of the superconductor and we show that, within our framework, the coherence length of the superconductor is related to the inverse of the gap size, just as in bulk BCS theory. The resulting local density of states (LDOS) in the superconductor is non-zero at the Fermi level due to the metallic host, giving it a striking resemblance to the pseudogap phase in copper-oxide based superconductors. Finally we investigate how magnetic impurities affect the superconducting state by embedding 3 rd row d-block magnetic impurities into bulk and surface Pb. In the presence of magnetic impurities, there is a pair-breaking effect that results in sub-gap Yu-Shiba-Rusinov (YSR) states which we decompose into contributions from the individual orbital character. In bulk Pb we find that not only are there two distinct YSR resonance pairs coming from the t2g and e g orbitals, there is a significant but smaller response from the 's' component of the impurity contributing to a third pair of YSR resonances. The intensity of the peaks is governed by the LDOS at the Fermi level of the impurity in the normal state. This finding is only reinforced when investigating how magnetic impurities, as an adatom and as an embedded impurity, affect the surface electronic structure. In both cases the degeneracy of the t2g and e g is further split, however in some cases no YSR resonances associated with 'd' orbitals are observed due to the majority and minority peaks being completely below or completely above the Fermi level. This highlights the important fact that multiple YSR states in the presence of 3d magnetic impurities cannot be attributed to the d-moment alone.

Moore's law predicts that the number of transistors on a computer microchip doubles every two years. As a society we focus on decreasing the size of our computers. As a result the transistors present on computers have been rapidly reduced in size over the past decade. We have now begun to infringe on the quantum regime, resulting in the need for the theoretical development and manufacture of quantum technologies. Current evidence suggests that the length of transistors on microchips will soon be as small as approximately fifteen atoms placed side by side, as such it is important that we are able to model molecular nanojunctions. A molecular nanojunction is a circuit which makes use of molecules as its building blocks, the molecule itself is attached to two electronic leads as a means of completing a circuit. The theoretical model for such devices must be able to accurately predict the behaviours of systems which couple to several environments. The central transport mechanism of the molecule is treated as a quantum system while the remainder of the molecule is modelled as a phonon bath. As such the electron-phonon coupling considered when electrons move through the molecule must be evaluated beyond the perturbative approach. Throughout this body of work we shall discuss and develop the reaction coordinate formalism, allowing for the incorporation of strong phonon contributions in our models. The strong vibrational coupling invalidates the additive treatment of our model and so we shall develop a non-additive master equation. Our non-additive master equation will properly account for the influence of strong and non-Markovian coupling. We shall extend our analysis to consider regimes where our molecular nanojunctions act as thermoelectrics. A thermoelectric device makes use of temperature gradients between the system and surrounding environments in order to overcome chemical potential or energetic barriers. Using a reaction coordinate formalism we will consider the impact of strong electron-phonon coupling on the properties of several thermoelectric regimes for multiple models. We shall finish our analysis by designing quantum refrigeration models and comparing their operations with classical emulators. Component cooling is a problem of considerable importance in the development of quantum technologies and through our work we aim to discover thermodynamic properties for quantum fridges while comparing and contrasting with their classical counterparts. Using counting statistics throughout our analysis we shall track particle and energy exchange to calculate current, noise, heat flow, power, efficiency and Fano factor as required. As a result we will be able to identify the importance of non-additive and strong coupling effects within molecular nanojunctions as well as determining the overlap between quantum fridges and their classical emulators.

This work discusses the relevance of the oxidation procedure on wide-band gap semiconductors and the effect that has on the surface chemistry. It has been shown that acid treatment procedures produce an incomplete termination resulting in a reduction in thermal stability. Pure oxygen anneals have been conducted on diamond surfaces and measured using Photoelectron Spectroscopy(PES) techniques in-situ at near ambient pressures and have shown that 400°C is an optimum temperature for the removal of sp2 carbon and achieving a complete oxygen coverage of the surface. The effect of surface termination of Detonation Nanodiamonds (DNDs) and single crystal diamonds have been studied experimentally and theoretically using PES and Density Functional Theory to determine the most stabilised terminations for device applications and drug adsorption. These have then been measured experimentally and molecule coverage has been characterised using optical scattering and absorption techniques.

This thesis proposes two theoretical models. The first theory that is devised extends a model suggested by Karnaukhov which suggests spontaneously broken time reversal symmetry (T-symmetry) in a superconductor, thus implying a non trivial topology with the system. The first contribution of this thesis provides an analytical derivation for such a system, in contrast to the original paper which relied on numerical techniques. The analytical solutions confirm the results of the original paper. Furthermore, the assumption of the translationally invariant gap field being homogeneous is checked. This yields the result that for zero chemical potential there is a degeneracy of ground states along the diagonals of the Brillouin zone, and thus it can not be claimed that the gap field is homogeneous in all cases. Consequently, it is found that T-symmetry may not be broken in the scenario for a zero chemical potential, but in all other cases it is. The other theory that is explored within this thesis is a quasi-1D model which is based on Luttinger liquid wires which have superconducting coupling inbetween the wires. From this a disorder term is added, and the relation between disorder and superconductivity is studied. This was inspired by an experiment which claimed that disorder could enhance superconductivity. To solve the model, renormalisation group (RG) theory is applied, and the coupled differential equations were solved. For certain initial conditions, it is found that disorder could enhance superconductivity, which represents a novel piece of research. Moreover, different mechanisms of how this phenomenon occurs are studied, by looking at the competition between charge density wave (CDW), spin density wave (SDW) and the normal state. In an attempt to fully reconcile the experiment with the theory, different properties of the resistivity are studied such that direct comparisons can be made between the predictions of the theory and the experiment itself.

This thesis describes investigations of copper-chalcogenide thermoelectrics and the application of advanced structural characterization techniques to explore structure-property correlations. An in-situ cell was designed and developed to study the electrical transport properties and structure of thermoelectric materials. It allows for the simultaneous collection of powder neutron diffraction data and electrical transport data as a function of temperature. An experiment on Cu₂.₁₂₅Ge₀.₈₇₅ZnSe₄ demonstrated that the cell can reliably monitor changes in the structure and thermoelectric properties. The in-situ cell was exploited to investigate n-type thermoelectric materials in the Cu-Fe-S system. A study of CuFeS₂ shows the influence of different structural phases on the Seebeck coefficient. Meanwhile, the origins of anomalies in the electrical transport property data of samples with compositions Cu₉Fe₈S₁₆ and Cu₉Fe₉S₁₆ are revealed. The observed local maximum in the power factors are linked to structural phase transitions over temperatures of T = 425 to 500 K. Total neutron scattering experiments on bornite (Cu₅FeS₄) reveal the nature of the copper and iron ordering within its three structural phases. The transition at ca. 475 K can be described by a partial disordering of the iron and vacancies, the transition at ca. 530 K leads to full disorder of the cations and vacancies. Following this, the thermoelectric performance of bornite was enhanced by introducing small deviations from the ideal stoichiometry. The thermoelectric figure of merit was improved from ZT=0.44 in Cu₅FeS₄ to ZT=0.79 in Cu₄.₉₆₈Fe₀.₉₇₂S₄ at 550 K. The low-temperature structure of the high-performance thermoelectric tetrahedrite (Cu²⁺)₂(Cu⁺)₁₀(Sb³⁺)₄(S²⁻)₁₃ has been determined and the Cu(II) species located within the structure. This has allowed the origin of the magnetic properties of the material to be understood for the first time. This collection of studies on thermoelectric copper sulphides will contribute to bringing us closer to realising low-cost, low-toxicity thermoelectric modules.

My research focuses on the modelling of excited states in organic semiconductors applied to three different areas, namely, optical spin injection singlet fission, and optical detection of polarons. One of the challenges in the field of spintronics is spin injection, which has been achieved optically in inorganic crystalline semiconductors, but not yet in organic semiconductors. Here, we apply group theory and computational methods to design molecular materials in which spin can be injected optically via circularly polarized light (CPL). When designing molecules for their optical excitation properties, additional design rules can be defined by considering the relationship between the symmetry of the molecule and its excited state properties using group theory. The theory reveals that molecules with C3h symmetry are good candidates, because they support circularly polarized transitions. Among the molecules with the correct symmetry using TDDFT calculation we are looking for candidates with low lying circularly polarized triplets corresponding to ms = +/-1 . To preserve the spin the triplet must be excited directly from the ground state, thus it is required to have a relatively high oscillator strength. We designed a series of molecules with C3h symmetry which were synthesized, some for the first time, by our collaborator. We present preliminary experimental validation of our approach with spectroscopic studies of the new family of molecules. The research shows how symmetry can be used in molecular design for spintronics applications. My second study concerns understanding the dynamics of singlet fission in organic semiconductors. Here I present a study on dynamics of singlet fission in diluted pentacene films and calculations which can explain the differences in quintet rates of dissociation between molecular pairs. We found out that the rate of the dissociation can be influenced by the degree of delocalization and charge-transfer character of the orbitals and excited states in the two different packing structures considered. My last study concerns understanding the behaviour of conjugated polymer electrodes operating in aqueous solution. We used calculations of absorption of polarons to quantify the depth of charge in polymer electrode. We used calculations of reaction potentials to identify likely side reactions that could limit the efficiency in the presence of oxygen.

Thermoelectric power generation presents an opportunity to `scavenge' energy that would otherwise be wasted as heat. Heusler alloys, a class of materials often comprising inexpensive, non-toxic elements, are promising for practical use in a new generation of thermoelectric devices. Recently, efficient thermoelectric Heusler alloys have overcome a performance-limiting thermal conductivity through the introduction of nanostructures that scatter phonons and impede thermal transport. However, the nature and stability of nanostructures can be difficult to discern, especially the minor compositional variations that derive from inhomogeneous phase segregation. Throughout this thesis TiNiSn, which forms the basis for some of the most promising n-type half-Heusler thermoelectrics, is studied through a unique combination of elemental and diffractive analysis in the scanning transmission electron microscope (STEM). Epitaxial thin films of TiNiSn are grown by pulsed laser deposition and FIB-prepared cross-sections of these are characterised in STEM with a focus on aberration-corrected STEM-EELS spectrum imaging and scanning precession electron diffraction (SPED), yielding precise chemical and structural quantification with nanoscale spatial resolution. The results throughout this thesis demonstrate the importance of STEM for quantitative studies of thermoelectric materials, as it can provide the analytical precision required for accurate identification of minority phases in TiNiSn specimens that would otherwise be overlooked in bulk analytical techniques. Sensitivity to very small elemental concentrations is a cornerstone of the use of STEM-EELS for chemical characterisation. Precisions of 0.3 % were achieved through adoption and development of refined, reference-based, absolute elemental quantification protocols which were essential in overcoming difficulties with large uncertainties posed by conventional methods. The success of this approach, in part, is due to advances made in characterisation of experimental conditions including, for the first time, an automated, standard-less approach to the measurement and correction of energy dispersion non-uniformities. Dispersion correction enables reliable, absolute calibration of energy-loss in spectra to yield a precision better than 0.1 eV. These developments in STEM-EELS were then used in three investigations of TiNiSn thin films exploring aspects of nanostructuring, phase segregation and crystrallographic strain and coherency. We discovered the spontaneous formation of nanostructures during thin film growth, gaining some insight into the phase segregation mechanisms that lead to their nucleation. Novel in situ STEM studies of phase segregation facilitated direct observations of the thermal evolution of nanoscale phases and results enabled characterisation of diffusion rates of Ni migration between full- and half-Heusler phases, for which the activation energy was calculated as 0.3~eV. Combining SPED with advances in detector technology, STEM structural investigations highlighted an interesting strain texture associated with nanostructuring of the half-Heusler thin films. Finally, combining SPED results with STEM-EELS measurements is proposed as a route to `correlative-STEM' analysis, which unifies nanoscale chemical and structural information for greater insights into the impact of nanostructures in thermoelectrics.

In recent years, organic semiconductors (OSCs) have generated many research interests from both academia and industry due to the exotic properties and potential applications in flexible displays, light-emitting diodes, solar cells as well as thermoelectrics. Compared with their inorganic counterparts, OSCs have several advantageous features including low cost, lightweight, mechanically robustness, ease of synthesis and tailoring material properties, environmental friendless, flexibility. For many of the mentioned applications, OSCs are doped to improve the conductivity. This is particularly important to improving the thermoelectric performance of OSCs and the figure of merit ZT. However, another equally important parameter, the Seebeck coefficient, tends to decrease when carrier concentration and conductivity increase. Therefore, it is crucial to find a balanced point where ZT maximizes. To achieve this, it is paramount to understand charge and entropy transport as well as the related key parameters affecting the electrical and thermoelectric properties in doped OSCs. Herein, doped poly(2,5-bis(3-tetradecylthiophen2-yl)thieno-[3,2-b]thiophene), PBTTT and its derivates are selected in this thesis for the investigation of thermoelectric and charge transport in highly conducting polymers. An unprecedented doping regime can be achieved via ion-exchange doping method, which is already approaching the metal-insulator (M-I) transition. The enhanced charge delocalization has been evidenced by the systematic spectroscopic as well as transport studies for samples with a broad range of conductivities. The clear Hall effect has been detected by a high-resolution ac Hall set-up, with the heavily doped sample showing a temperature-independent Hall coefficient, which indicates nearly "ideal" band-like transport. The temperature dependences of conductivity and Seebeck coefficient for samples at different doping levels witness the onset of metallic states evolved from pure hopping transport. The Seebeck coefficient over a wide range of conductivity can be analyzed by a model that accounts for the energy dependence of the transport function and show a transition from an exponent s=3 to s=1 or 2. Such a transition also correlates to the point where power factor maximizes. We correlate these observed transport phenomena for ion-exchange doped PBTTT with microstructural ordering as function of increasing doping levels, as supported by the diffraction data. Moreover, side-chain modification and chalcogen substitution have been established to affect the properties of semiconducting organic materials. In this thesis, we also investigate their effects on doping as well as electrical and thermoelectric properties. The adopted polar side chain modification with alkoxy and glycol groups was verified to give more efficient doping but show an adverse effect on thermoelectric and electrical performance. Intriguingly, the introduction of single chalcogen atom into the polymer backbone, which is believed to enhance the interchain interaction, gives rise to decent electrical and thermoelectric properties for doped samples. We attribute such improvement to the peculiar microstructures induced by the heteroatom. The presented fundamental studies of both charge and thermoelectric transport properties on doped semi-crystalline polymers aim to contribute more insights into the structure-property relationship in conducting polymers and thus provide guidelines to improve electric and thermoelectric properties of organic materials for future applications.

In this thesis superconductivity with unconventional pairing symmetries arising from repulsive interactions is investigated. Anyonic quasiparticles within the subclass of chiral p-wave superconductors are also examined. In Chapter 2 we study weak-coupling superconductivity in a repulsive Hubbard model on the tetragonal lattice. With the weak-coupling approximation we establish the superconducting phase diagram as the out-of-plane hopping strength and electron filling is varied. For four Fermi surface topologies we identify a total of five types of p- and d-wave ground state orders, several of which have accidental line nodes and break time-reversal symmetry. The weak-coupling scheme is adapted to strontium ruthenate (Sr₂RuO₄) in Chapter 3. We compute and compare odd- and even-parity superconducting order parameters using a realistic three-dimensional band structure. Two superconducting phases are identified: a helical p-wave spin triplet and a d-wave spin singlet phase. Both orders are roughly found to be compatible with specific heat data and recent nuclear magnetic resonance measurements [A. Pustogow et al., Nature 574, 72 (2019)]. We suggest that a d-wave order is likely involved in the superconducting phase, although certain experiments appear to remain incompatible with this conclusion. In Chapter 4 we describe anyonic (Majorana) quasiparticles in chiral p-wave superconductors at temperatures non-negligible compared to the superconducting gap. We consider the impact of thermally occupying in-gap vortex states on the hybridisation of two Majorana modes. The hybridisation, reflecting the state of the qubit defined by the two Majorana modes, is found to decay algebraically with temperature just above the first-excited state energy scale. In novel iron-based superconductors our results suggest that there is an appreciable temperature range in which qubit read-out can be achieved via the inter-vortex force derived from the hybridisation.

Organic semiconductors are quietly revolutionising the modern world, finding application in light-emitting diodes, thin-film transistors and photovoltaics. However their short device lifetimes and reduced power-conversion efficiencies have limited their commercial uptake. Both experimental and computational work to find new materials and architectures and study of their charge transport properties continues. Computational studies of the charge transport properties of organic semiconductors depend heavily on the structure/morphology. Structures are often assumed to be a regular lattice, even in the case of amorphous materials, with some groups using molecular dynamics (MD) and Monte Carlo (MC) methods to capture the disorder. However these approaches have significant drawbacks, some of which are technical (MD and MC can be computationally arduous at large system size) and some of which are physical (below the glass transition, the energy landscape makes it difficult to sample a large number of states). Other approaches such as coarse-grained and basin-hopping methods attempt to overcome these problems but often create new problems such as the need to develop new force-fields, having to regain full-atomistic representation of molecules afterwards, and still being hindered by the landscape. In this work, a new method, Simulation of Atomistic Molecular Structures using an Elastic Network (SAMSEN), is proposed and applied to molecular and polymeric systems. SAMSEN contains both a structural and dynamical model that individually attempt to overcome the technical and physical problems of current methods. The structural model requires that molecules are split into rigid sections, which retain their atomistic representation and are constructed to interlock with their neighbouring sections, and restrict the maximum displacement of atoms from their locally optimised positions. Atomic collision rules, limiting minimum separations, are also enforced. This combination allows SAMSEN to recreate the short-range structure of weakly-interacting non-polar small molecules. The dynamical model creates an elastic network between the rigid sections and displaces them across the low-frequency vibrational modes to achieve collective large-scale motion and computationally-fast structural relaxation. SAMSEN is applied to systems of spheres to study the structural and dynamical parameters and a regime is found where a band of collective low-frequency modes can be found, sampling rate can be increased without altering structure and the mean overlap of atoms can be controlled without altering the sampling rate. The structural parameters are determined entirely by the class of system being studied, leaving the dynamical parameters to be chosen to maximise sampling rate. SAMSEN is then applied to systems of small molecules and is shown to be widely applicable, providing good approximations to the short range structures produced by full atomistic force-field methods. SAMSEN phenyl-C61-butyric acid methyl ester (PCBM) states are found to have structures close to those of the higher energy minima in a potential energy landscape of an all-atom potential and the distribution of these potential minima is found to be near-Gaussian. SAMSEN outputs are then used as inputs of MD simulations, recreating the full-MD structures and quickly finding the lower-energy minima. This method provides a useful pathway for those interested in sampling the distribution of morphologies at equilibrium. The diffusion of electrons is simulated for each state in the distribution of MD and SAMSEN inherent structures and it is found that the diffusion constant is near independent of the potential of the minima, despite short-range structural differences. Turning to polymers, the coarse-graining into rigid sections now controls the relative structure between repeat units. The structure and vibrational modes of poly(3-hexylthiophene) (P3HT) is studied in the pure amorphous phase and also when blended with PCBM. Increased persistence of the P3HT backbone is found upon mixing with PCBM but the density of neighbouring chains is unaffected up to the miscibility limit. Studying the long time (low frequency) modes, the rate of relaxation of the P3HT backbone is slowed by the addition of PCBM due to a shift in frequencies, rather than a change of collective behaviour of the individual modes. The excitonic transport properties of P3HT are then studied in the amorphous and crystalline phase in a transfer matrix approach, finding the exciton diffusion length in the low charge limit and comparing to experimental and previous computational work on P3HT nanoparticles. Low disorder polymer, Indacenodithiophene-co-benzothiadiazole (IDT-BT), is also studied, with a morphology generated, the inter-molecular transfer integrals calculated using a quantum chemistry package and the diffusion constant for holes determined for a range of intra-molecular transport rates. Comparing the hole diffusion constant to experimental and computational work, an estimate of the intra-molecular transport rate is made. This work serves as a framework for researches interested in determining the structures, long-time vibrations and charge transport properties of weakly-interacting amorphous organic semiconductors where samples of states if required. It can achieve this without molecule-specific parameters or forces and does so at modest computational cost and therefore opens the possibility of sample a large number of states of simulating bigger system sizes (approaching device scale) without requiring access to high-performance computing resources. Further opportunity exists to constrain the dihedral angles, consider electrostatic interactions, as well as to study the charge transport properties of polymer systems incorporating an accurate model for intra-chain charge-transport.

Since the discovery of superconductivity in LaFePO, numerous iron-based superconductors have been identified within diverse structure families. Superconductivity in the layered iron germanide YFe₂Ge₂ was first reported in 2014. It stands out from the commonly known iron-based superconductor families for not containing either Group-V or Group-VI elements and has since been predicted to be an unconventional superconductor. The intermetallic d-electron system YFe₂Ge₂ exhibits an unusually high Sommerfeld coefficient of ≈SI100 millijoule/mole kelvin², signalling strong electronic correlations. Its low-temperature normal-state resistivity displays a T¹.⁵ power-law temperature dependence, which is an indication of non-Fermi-liquid behaviour. While superconductivity in YFe₂Ge₂ has been widely observed below T_c ≈ SI1.9 kelvin in electric transport measurements, evidence of a bulk superconducting transition has proved elusive. This has prompted significant efforts into improving the crystal quality. In this thesis, I present the crystal growth methods which have successfully produced high-quality poly- and single-crystal YFe₂Ge₂ samples. Measurements on these samples have led to conclusive evidence that superconductivity is an intrinsic property of this compound. Disorder effects on both the poly- and single-crystals have been studied through structural investigations, in which anti-site disorder of germanium substitution on the iron site was found to be the dominant factor. The fast suppression of the superconducting transition temperature, T_c, of YFe₂Ge₂ by disorder suggests an unconventional pairing mechanism. Using a liquid transport flux method, single crystals with residual resistivity ratios ($\mathrm{RRR} = \mathrm{\rho}_{\SI{300}{\kelvin}}/\mathrm{\rho}_{\SI{2}{\kelvin}}$) reaching 470 have been synthesised. These crystals exhibit clear bulk superconducting transitions. Low-temperature specific heat and $\mu$SR measurements performed on these crystals provided evidence for multi-gap superconductivity, most likely of the s^pm-wave nature, which is compatible with theoretical predictions. Moreover, quantum oscillations have been detected for the first time in dHvA susceptibility and tunnel-diode oscillation measurements of high-quality YFe₂Ge₂ single crystals. Although unable to account fully for the high Sommerfeld coefficient, the current results have confirmed significant mass enhancements in the detected Fermi surface sheets.

Three standard reference material Nb-Ti strands, manufactured for the ITER poloidal field magnets, were extensively characterised using both transport and magnetisation techniques, with a focus on the behaviour of the material in a magnetic field. To quantify the effect of magnetic self-field, the field generated by current flow, the critical current density was measured as a function of the applied magnetic field, temperature, current polarity, and geometry. A high capacity probe was designed and commissioned for the transport measurements. The characterisation in different measurement geometries was possible with custom-built sample holders (i.e., barrels). As the titanium alloy Ti-6Al-4V used in the standard ITER VAMAS barrel is superconducting at 4.22 K, an alternative titanium alloy (Ti-6Al-2Sn-4Zr-2Mo-0.2Si) was identified that is not superconducting at 4.22 K and used to manufacture the barrels. The transport measurements at low applied magnetic-fields resulted in high current densities, and the effect of self-field being large. To investigate the self-field both finite element analysis (FEA) and semi-analytic methods were employed. The H-formulation of Maxwell’s equations was implemented using Comsol Multiphysics, a commercial FEA software. The model input for the superconductors properties were defined using a number of experimental J_C (B) relationships. The architecture of the strand was approximated with different degrees of complexity. The FEA models considered the cross-section of the strand as circular, annular, and as three nested cylinders (i.e., tubes-within-tubes). The probability distribution of the magnetic field components in the superconducting domain was calculated and analysed. The changes in the field distribution due to the geometry of the measurement barrels and the current orientation, (resulting in opposite Lorentz force orientation), were used to quantify the magnitude and orientation of the self-field. A semi-analytic method was used to derive a the magnetic field distribution data from the FEA and the experimental data. The resultant piecewise J_C (B) calculated for the Nb-Ti strand, can be considered a universal J_C (B) relationship.

The energy level tuning effect, observed when mixing halogenated versions of similar molecules, has recently been identified as a new way to modify the bulk ionisation energy and electron affinity of an organic semiconducting thin film, and increase the open-circuit voltage in organic solar cells. In this thesis, the energy level tuning effect is extended to organic field-effect transistors (OFETs). A method for the fabricating ambipolar devices with balanced hole and electron transport is established. This is achieved by using blends of two host molecules, zinc phthalocyanine (ZnPc) and its eight-times fluorinated derivative (F8ZnPc), with energy levels that shift based on mixing ratio. The semiconducting behaviour of the bottom-gate bottom-contact OFETs can be tuned continuously from unipolar p-type, through ambipolar, and finally to unipolar n-type. For the ambipolar devices, the optimum balance between the hole and electron mobilities is found for the blend of 1:1.5 weight ratio of ZnPc:F8ZnPc with hole and electron mobilities of (8.3 ± 0.2)×10 −7 cm2V−1s−1 and (5.5 ± 0.1)×10−7 cm2V−1s−1 , respectively. An application of the ambipolar devices in a complementary-like voltage inverter circuit, with performance comparable to an inverter based on separate ZnPc and F8ZnPc OFETs, is demonstrated. Next, a p-dopant (F6-TCNNQ) is introduced into the blend of ZnPc: F8ZnPc to investigate the impact of the energy level tuning effect on the molecular doping process. The doping efficiency is investigated using photothermal deflection spectroscopy and electron paramagnetic resonance spectroscopy, and is found to depend upon host mixing ratio. The experimentally observed trend is explained with a statistical model that includes both shifts of the host’s ionisation energies, and, importantly, the electron affinity of the dopant. The energy level shift in the model is in close agreement with the 0.86 eV shift in ionisation energy observed experimentally. As further validation, the model reproduces the measured trend at low temperature. The energy level tuning effect therefore has a crucial impact on the molecular doping process. The practice of comparing host and dopant energy levels must consider the long-range electrostatic shifts to consistently explain the doping mechanism in organic semiconductors.

This thesis presents new high-resolution resonant inelastic x-ray scattering (RIXS) studies in high-Tc cuprate superconductors (HTSs). RIXS measures elementary excitations of the type which characterise the ordered phases known to exist alongside superconductivity in the cuprates. The role that these phases play in the pairing mechanism which gives rise to superconductivity remains unclear. The work in this thesis therefore presents new measurements of the excitations with the aim of helping to constrain theoretical models of pairing. Spin fluctuations are characteristic of the antiferromagnetic phase of cuprates but are also seen to persist into superconducting phases. As a result, theories based on the Hubbard model often consider spin fluctuations to be important to pairing. The role of charge fluctuations, either competing or contributing to superconductivity, is also important to understand. The experimental work was performed at two new RIXS spectrometers, I21 at Diamond Light Source and ID32 at the European Synchrotron Radiation Facility, both optimised to achieve high intensity and energy resolution in the soft x-ray RIXS regime. Measurements are presented on single layer cuprate La2CuO4 where consideration of the prefactors to the RIXS intensity reveals the wavevector dependence of the dynamical susceptibility in new regions of the Brillouin zone. The measurements are extended to two doped compositions of La2-xSrxCuO4, x = 0.12 and 0.16. The spin fluctuations are characterised within a damped harmonic oscillator model which reveals the wavevector dependent anisotropy of the damping in doped compositions. New RIXS measurements in two-layer YBa2Cu3O6-x (YBCO) show similar effects. The charge order is also examined in YBCO revealing a broad wavevector dependent peak in the elastic intensity. This work is also a test of RIXS as a probe of low-energy excitations in well studied cuprate materials and provides insights into the RIXS intensity by comparison with a similar probe: inelastic neutron scattering.

The properties displayed by the large family of layered materials is vast, and can range from semiconducting (MoS2) to superconducting (NbSe2) and ferromagnetic (CrBr3). Remarkably, the properties of these materials are often dramatically changed when they are exfoliated down to a single atomic layer, where quantum confinement can play a significant role. However, many of these materials are highly reactive towards oxygen and water present in the atmosphere. In bulk, a passivation layer usually forms which protects the interior of the material from further corrosion (the same mechanism which protects stainless steel). However, if we want to study pristine atomically-thin layers we need to develop protocols for handling these air-sensitive materials in a controlled atmosphere. In the first half of this thesis, we use a state-of-the-art system for the handling and fabrication of the air-sensitive layered superconductor NbSe2 and layered ferromagnet CrBr3 into heterostructures and investigate their properties at the two-dimensional limit. In the latter half of this thesis we study graphene/hexagonal boron nitride heterostructures using two newly developed scanning probe techniques. Here, not only did we require high-mobility samples but also large contamination free areas. Additionally, the surface of these structures is devoid of any postfabrication residues. We use a scanning single-electron transistor to map the two-dimensional electron flow, and by tuning the electron carrier density we are able to observe the shift from diffusive to ballistic transport with high sensitivity and minimal invasiveness. Also, we use a scanning superconducting quantum interference device as an ultra-sensitive thermometer to elucidate the heat dissipation mechanisms in high-mobility graphene/hexagonal boron nitride samples. We observe, for the first time, resonant inelastic scattering between electrons and localised atomic defects.

In this thesis, we present a study on thin films and organic field effect transistor (OFET) devices using solution ageing induced aggregation and soft lithography techniques. We first investigated the effect of solution ageing and film thickness of F8T2 (poly(9,9-dioctylfluorene-co-bithiophene)) spin coated from different boiling point solvents. Using the weakly interacting H-J aggregate model, we found that with solution ageing, there was an increase in J-aggregate ordering, characteristic of the beta-phase regime commonly associated with polyfluorenes. In organic transistor devices, this corresponded with a positive correlation with threshold voltage, V_th, and the Vissenberg and Matters density-of-states temperature for disorder, T_0. Azeotropic binary solvent thin films of F8T2 were also investigated in regimes of extreme H and J aggregation, with the latter indicating more presence of the beta-phase was detrimental to OFET performance. Using the soft lithographic approach, patterning of the organic semiconductor layer was achieved by applying the micromolding in capillaries (MIMIC) and solvent assisted micro molding in capillaries (SAMIM) methods. Different architectures of stamp designs and domains using Fluorolink MD 700 perfluoropolyether (PFPE) and polydimethylsiloxane (PDMS) materials were investigated and their effects on OFET device performance are presented. We found that patterned organic semiconductor layers of both small molecules such as TIPS-pentacene (6,13-bis(triisopropylsilylethynyl)pentacene), and the polymers F8T2 and P3HT (poly(3-hexylthiophene)) from a solution precursor, were capable of forming sub-micron features using optimised stamp geometries and materials at room temperature. Furthermore, we also investigated the effect of confined crystallisation of F8T2 from mono and azeotropic binary solvents in staggered top gate geometries. Using the highly hydrophobic fluoropolymer CYTOP as the dielectric, saturation mobilities of >0.001 cm^2/Vs, threshold voltages of V_th > -20 V, and gate leakage currents of (|I_D/I_G| > 10^3) were obtained. These results for confined crystallised F8T2 OFETs are of better performance, with the mobility in particular being an order of magnitude higher than that of conventional solution processed counterparts using spin coating and drop casting deposition methods.

The unconventional class of superconductivity comprises a broad range of materials with vast potential for applications in solid state devices. Unconventional superconducting states are capable of supporting a range of exotic properties, such as intrinsic magnetism, anomalous transport and non-trivial topology, making them ideal candidate materials for many fields, particularly those of spintronics and quantum computation. Harnessing these properties remains challenging as such materials are not yet fully understood, and thus the potential of this class remains largely untapped. The work presented here is focussed on chiral superconductors, a type of unconventional superconducting material in which the Cooper pairs form with an intrinsic magnetic moment. Interplay between the magnetisation associated with a chiral order parameter and the transport properties of superconductivity provides a rich platform for the emergence of unique and anomalous phenomena. The intent of this investigation is to derive a broad set of tools with which to study such phenomena in a general superconductor. Key among the results is the derivation of a modern theory to calculate the total orbital magnetic moment generated by the formation of a superconducting state with a chiral order parameter. Also presented are studies of the anomalous Hall and Kerr effects, which are phenomena deeply linked to the orbital moment. A comprehensive understanding of the shared origin of orbital magnetism and anomalous transport is developed through an analysis of the relation of these properties to the Berry curvature of the intrinsic bandstructure. As a physical platform on which to test and analyse these general theories, two distinct tight-binding models of the proposed p-wave superconductor Sr2RuO4 are presented and utilised for model calculations. The exact form of the order parameter in this material remains a source of fierce debate, and the comparison of the two models provides a method with which to study the origins of the key properties of the state from the structure of the gap. It is demonstrated that multi-band effects are essential in the description of the intrinsic phenomena in Sr2RuO4, and that the spin-orbit interaction plays a vital role in generating these properties. An outstanding issue in the identification of the order parameter in Sr2RuO4 is that p-wave symmetry is expected to induce large edge currents, which have not been observed experimentally. The results obtained here provide possible explanations for this perceived contradiction. Also shown are a range of factors which suppress the magnetisation associated with itinerant currents, such as the presence of superconducting gaps on multiple bands with inter-orbital pairing, the influence of the spin-orbit interaction and the addition of longer range pairing terms in the gap structure. Work remains to be done to irrefutably resolve these issues, but an essential foundation is established through the theoretical work presented here. Finally, the groundwork for a number of avenues for further study is laid, including the fine-tuning of the extended pairing model of Sr2RuO4, the study of anomalous phenomena in other chiral superconductors and the generalisation of the finite-temperature contributions to the orbital moment in a superconductor.

Assembling two-dimensional materials in vertical stacks—van der Waals heterostructures—leads to the creation of new properties and functionality in these systems. Electromagnetic and thermal effects in van der Waals materials, particularly the use of these effects for mechanical actuation, remains largely uncharted. Therefore, exploring electromagnetic and thermal actuation in van der Waals heterostructures is the main aim of this thesis. A range of existing nano- and microfabrication techniques was optimised to improve both quality and performance of the devices made of van der Waals heterostructures. Heterostructures made of graphene encapsulated by hexagonal boron nitride (hBN) were fabricated using a modified microfabrication procedure to produce much cleaner graphene-hBN interfaces. Bright light emission from graphene induced by incandescent heating was demonstrated and characterised using multiple techniques, including Raman spectroscopy and transport measurements. The results of this study reveal that boron nitride provides a protective environment for graphene hot filaments, thereby enabling a prolonged light emission and operation at temperatures exceeding 2000 K. Then, the quality of hBN/graphene heterostructures was explored further by fabrication and characterisation of tunnelling transistors based on graphene/hBN/graphene heterostructures. In particular, the defects that exist within the hBN flakes used as a dielectric layer for graphene-based tunnelling transistors were exploited for probing the density of states in graphene electrodes. Diverging from graphene-hBN systems, the behaviour of water in a common layered mineral like gypsum was explored by adopting a simple measurement procedure. This was motivated by recent results on unusual dielectric permittivity of confined water molecules. Capacitance measurements were performed for water confined in two different systems—in nano channels fabricated by the use of 2D materials and in gypsum (CaSO4-2H2O) system. Electrostatic actuation was studied in various fabricated designs of 2D materials heterostructures including microelectromechanical systems based on graphite/hBN/graphite capacitors. Moreover, atomic force microscopy technique was used to attempt to initiate transition between ABA and ABC stacking in graphite films. It was found that AFM nanoindentation indicates insufficient capability of achieving this transition.

This work details the fabrication and measurement of various two-dimensional (2D) material light emitting diodes, constructed as heterostructures of graphene, hexagonal boron nitride and transition metal dichalcogenide (TMD) monolayers. Devices are created for two different projects in order to study two interest topics currently at the forefront of 2D materials research: interlayer excitons (IXs) and single photon emitters (SPEs). For the IX studies, devices are fabricated in order to electrically inject electrons and holes into a type-II band alignment heterojunction formed from WSe2 and MoS2 monolayers. Electroluminescence measurements of the devices demonstrated the formation and emission of the expected interlayer exciton, between the two K/K' points of the materials. The observed emission is confirmed to be the interlayer exciton by its bias dependent emission energy, which undergoes a blueshift to higher energies as the bias is increased. This behaviour is explainable by considering how the relative band alignment of each material shifts with increasing bias. In addition, an upconversion process arising from IX-IX interactions is also observed in three of the devices and a similar upconversion-like process in one more. In this case, IX-IX interactions allow the population of intralayer exciton states in each TMD at biases where direct electrical injection into these states is not possible. A mechanism for this is proposed by which a large population of charge carriers may be achieved due to the different positions of the K/K' points in the two TMDs, making radiative recombination unfavourable. For the SPE project, a method of fabrication is developed, building upon previous reports, in order to purposely induce SPEs in specific locations of WSe2 and WS2 which could then be transferred to other locations while retaining the SPEs. The second half of Chapter 6 discusses photoluminescence and electroluminescence phenomena observed in an LED fabricated using the developed method. Narrow peaks indicative of SPEs are observed with a wide range of different bias dependent and magnetic field dependent behaviours. These different behaviours are quantified in that section.

The physics of superconductor-semiconductor hybrid junctions is governed by a combination of the macroscopic quantum coherence of superconducting systems and the mesoscopic physics inherent to semiconducting devices and Andreev bound states are the microscopic states which mediate transport through these junctions. In this thesis a series of experiments aimed at understanding Andreev bound states in Josephson junction devices are presented. RF reflectometry measurements of a superconducting tunnel junction are made sensitive near the high tunnel resistance by an impedance transforming tank circuit which can be adapted for different device resistances. The reflectometry measurement corresponds well with DC transport data meaning this technique can measure Josephson junction dynamics at high frequency. Progress is made towards more transparent superconducting contacts to CVD graphene for graphene Josephson junctions however switching to an epitaxial Al / InAs 2DEG material bypasses the contact transparency issue. Signatures of transport mediated by Andreev bound states in the few mode regime are observed in quantum point contact devices made from this material allowing the possibility of controlling and measuring single Andreev bound states. Josephson junctions coupled to superconducting resonators are measured using microwave frequency detection and DC transport. Andreev bound states in the few mode regime are observed via their effect on the resonator frequency suggesting that Andreev bound states in this material can be coupled to a resonator allowing measurement and control.

This thesis is composed of three projects including the AC magnetic susceptibility study of high-temperature superconductor YBa$_2$Cu$_3$O$_{7-\delta}$, the ionic-liquid gating study of the Mott insulator Sr$_2$IrO$_4$, and the single-electron study of quantum dot device with self-assembled nanocrystal PbS. Chapter 1 covers a general introduction to all three projects. The basic background and the motivation for each project are presented. Project I is covered in Chapter 2, Chapter 3, and Chapter 4. The first part of Chapter 2 is a theoretical introduction to the Bardeen-Cooper-Schrieffer theory of superconductivity with its main conclusions presented. This chapter builds a basis for the use of high pressure technique to YBa$_2$Cu$_3$O$_{7-\delta}$ in the later chapters. The rest of Chapter 2 reviews the work in the study of high-temperature superconductors, especially on YBa$_2$Cu$_3$O$_{7-\delta}$, on both experiments and theories and the possible applications of high-temperature superconductors. Chapter 3 introduces the YBa$_2$Cu$_3$O$_{7-\delta}$ sample preparation process and the characterisation. A dry cryomagnetic equipment was employed for the measurement. The results and the discussion are presented in Chapter 4. Project II is described in Chapter 5, Chapter 6, and Chapter 7. Chapter 5 firstly introduces the background knowledge of the gated material SrTiO$_3$ and the technical details of the ionic-liquid gating technique. Then the sample growth and the characterisation are presented. The fabrication process of Sr$_2$IrO$_4$ and SrTiO$_3$ (material for a control experiment) are described in Chapter 6. Chapter 7 covers the measurement and the result of the fabricated devices and related discussion. Project III ranges from Chapter 8, and Chapter 9. A literature review of quantum-dot devices and self-assembled nanocrystals is presented in Chapter 8. The experimental design of this nanocrystal quantum dot device is also included. Following it, the fabrication process of quantum-dot devices and the techniques used for fabrication are introduced in the start of Chapter 9. Chapter 9 also gives a description of the probe-station for measurements. The results and discussion of the measurements are covered in the last section of Chapter 9. Chapter 10 summarises and concludes the three projects stated above and gives some suggestions about the directions for future work.

Organic semiconductors exhibit exceptionally long spin lifetimes, and recent observations of the inverse spin hall effect as well as micrometer spin diffusion lengths in conjugated polymers have spiked interest in employing such carbon-based materials in spintronics applications. The charge transport and photophysics of organic semiconductors have been intensely studied for optoelectronic applications, revealing subtle relationships between molecular geometry, morphology and physical properties. Similar structure-property relationships remain mostly unknown for spin dynamics, where the charge carrier spins couple to their environment through hyperfine (HFI) and spin-orbit interactions (SOC). HFIs provide a pathway for spin relaxation while SOC plays a dual role in such materials: it couples the spin to its angular momentum and therefore enables both spin-to-charge conversion and spin relaxation. Understanding the molecular SOC, and finding a means to tune its strength, therefore is fundamentally important for materials design and selection. However, quantifying SOC strengths indirectly through spin relaxation effects has proven difficult due to competing relaxation mechanisms. We initially present a systematic study of the g-tensor shift in molecular semiconductors and establish it as a probe for the SOC strength in a series of high mobility molecular semiconductors. The results demonstrate a rich variability of molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We then correlate the above g-shifts to spin-lattice relaxation times over four orders of magnitude, from 200 µs to 0.15 µs, for isolated molecules in solution and relate our findings to the spin relaxation mechanisms that are likely to be relevant in solid state systems. Isolated molecules provide an ideal model system to investigate a spin's interactions with its environment but device applications commonly employ thin films. The second half of this thesis investigates polaron spin lifetimes in field effect transistors with high-mobility conjugated polymers as active layers. We use field-induced electron spin resonance measurements to demonstrate that spin relaxation is governed by the charges' hopping motion at low temperatures while Elliott-Yafet-like relaxation due to short-range, rapid spin density dynamics likely dominates high temperature spin lifetimes. Such a microscopic relaxation mechanism is highly sensitive to the local conformation of polymer backbones and we show its dependence on the degree of crystallinity in a polymer film.

In this thesis the synthesis, structure, and ionic conductivity of the sodium and lithium lanthanide pyrosilicates, A3LnSi2O7 (A = Li, Na; Ln = Gd-Er, Y), are reported. The Na- silicates, Na3LnSi2O7, were made by the ceramic method. The meta-stable Li-silicates, Li3LnSi2O7, were formed by a molten salt ion exchange of Li+ for Na+ in Na3LnSi2O7. Structural models for the two compounds were refined against powder X-ray and neutron diffraction data using the Rietveld method, and Fourier difference maps were used to identify the location of the lithium ions in Li3LnSi2O7. The refined structural models show that both alkali compounds are characterised by the P63/m space group and exhibit the same LnSi2O7 framework but possess a remarkably different arrangement of alkali ions. The Na-compounds exhibit four crystallographically distinct alkali-sites whereas the Li-compounds exhibit two such sites, only one of which is equivalent to that in the Na-structure. The new lithium site inhabits an atypical square planar environment. These structural models were corroborated by pair distribution function analysis, bond length analysis, and bond-valence calculations. Potential conduction pathways within the A3LnSi2O7 structures were identified with bond-valence methods and used to propose conduction mechanisms for alkali ion trans- port. Variable temperature impedance spectroscopy measurements were used to show the Li-silicates exhibit an ionic conductivity significantly greater than that of the Na-silicates. The maximum ionic conductivity measured in the Na-compounds was 1.08(7)×10−7 S/cm at 285.5(3) ◦C in Na3HoSi2O7, while that measured in the Li-compounds was 6.7(6)×10−6 S/cm at 286.17(14) ◦C in Li3HoSi2O7. A variable temperature impedance control system was developed to enable these measurements. A microcontroller was used to automate the measurement process; a custom software library was written to allow a user to orchestrate the process with a simple program; and a least squares fitting algorithm was implemented to allow for batch data analysis. This work may be further adapted to accelerate the discovery of new solid state electrolytes for application in all solid state batteries.

This thesis investigates some of the physics of semiconducting low-dimensional structures at low temperatures, as well as investigating the effects of defects on low-dimensional structures and magnetic fields on charge recombination in organic photovoltaics (OPVs). The applications of the systems studied vary from photodetectors, to LEDs, lasers and solar cells. We synthesised Cs2CuCl4 and CsCuCl3 nanoparticles. By varying the ratio of coordination solvents in the synthesis we can control the composition and morphologies of the fabricated nanoparticles, including dots, rods and wires. These nanocrystals showed broadband green emission upon excitation with sub-300 nm radiation, which we showed was due to emission from an intra-band Cu(II) defect. We also fabricated a variety of alkylammonium lead iodide materials. We found that hexylammonium lead iodide and dodecylammonium lead iodide emit broadband red light at low temperatures due to a Frenkel defect (f-centre). Additionally, we see evidence of biexciton emission in dodecylammonium lead iodide films at high excitation densities below temperatures of 225 K. The films in this study were seen to adopt two coexistent phases of dodecylammonium lead iodide, both a monoclinic P121/a structure and an orthorhombic Pbca structure, at room temperature. These films were used as the gain medium in a biexciton vertical cavity laser. This device was constructed from a distributed Bragg reflector coated with dodecylammonium lead iodide, a poly(methylmethacrylate) spacer layer, and an evaporated silver mirror. The onset of lasing was seen at 5.6 × 1018 excitations/cm3 at 75 K. Finally, the modulation of open-circuit voltage and short-circuit current by applied magnetic field in OPV devices made from PIDTPhanQ and PC(71)BM was investigated. We saw that magnetic fields influenced the recombination of charge-transfer (CT) states, and simulations indicated that the formation of CT states had a significant contribution from the bimolecular recombination of free charges. The simulations also showed that singlet CT state lifetimes were much smaller than triplet CT state lifetimes.

The intriguing properties of organic semiconductors in various optoelectronic applications, ranging from molecular wires for integrated circuits, to organic photovoltaics (OPV), organic transistors (OFET) and organic light-emitting diodes (OLEDs) have motivated the work presented in this thesis. More precisely, this thesis focuses on narrow energy gap materials, suitable for OLEDs emitting in the red and near-infrared (NIR) regions. Conjugated materials emitting at low energies face great challenges to have efficient light emission. This thesis proposes two very interesting and novel strategies to cope with the limiting factors of efficient light-emission from conjugated compounds. Firstly, a series of porphyrin oligomers is presented. With emission ranging from red to pure NIR, three architectures of these oligomers were studied. Zinc oligomers at various length that allowed for fine tuning of the emission, five hexamers with different coordinating metals at the centre of each unit, allowing for phosphorescence emission, and a pentamer, with single acetylene instead of butadiyne bonds connecting porphyrin units, resulting in a shorter oligomer with an extended pi-conjugation and a bathochromic shift of the emission. Two limitations can be identified for efficient NIR emission, the so-called 'energy-gap law' and aggregation quenching. Both limitations are addressed, resulting in unprecedented external quantum efficiencies when the oligomers are used in OLEDs and remarkable devices lifetimes, considering the non-optimised diodes. Secondly, three diketopyrrolopyrrole-based copolymers are presented and their photophysical properties discussed. These polymers represent a different strategy to prevent aggregation; by engineering covalent bonds, the conjugated core is sheathed within its cyclic sidechains. The strategy is proven highly successful and the three polymers are compared with their unprotected counterparts, where emission is severely quenched. The advantages of the encapsulation are more pronounced when the polymers are incorporated in OLEDs, where the encapsulated ones achieved up to 16 times higher external quantum efficiencies compared to the unprotected ones.

The Coulomb gas is a ubiquitous concept not just in physics but in many other fields of science, including chemistry, biology and engineering. In this thesis I make use the concept of the ``generalised'' Coulomb gas, which extends the concept of the ``traditional'' Coulomb gas by allowing more general solutions to Gauss' law without changing its fundamental thermodynamic properties. The generalised Coulomb gas was first introduced by Maggs and collaborators, who used it to develop a fast local simulation algorithm for Coulombic systems by taking advantage of the fact that the thermodynamics are unchanged. Further studies were conducted by Faulkner, who studied the generalised Coulomb gas not just for its intrinsic interest but also in the context of the XY model of magnetism, which maps to a 2D generalised Coulomb gas. I perform numerical studies of the generalised Coulomb gas, paying particular attention to the calculation of its field correlations; surprisingly, these have not been supplied before in the literature. These correlations can be separated into Helmholtz-decomposed components in order to extract the correlations of the traditional Coulomb gas, which are contained within those of the generalised system. I calculate field correlations in the 2D generalised Coulomb gas in the grand canonical ensemble in all regions of its phase diagram, which was given by Lee and Teitel and includes two Berezinskii-Kosterlitz-Thouless transitions, a first-order gas-solid transition and an Ising solid-liquid transition. I also perform analogous simulations of the harmonic XY model of magnetism, following the work of Faulkner, and show that it is the generalised Coulomb gas rather than the traditional one which provides a natural description of the emergent Coulomb physics therein. Lastly, I show preliminary simulations of the 2D canonical and 3D grand canonical generalised lattice Coulomb gases on the square and simple cubic lattices respectively, and suggest further work, including the possibility of performing simulations on the diamond lattice in order to make closer contact with spin ice physics.

This thesis presents a study on a series of layered transition metal-based superconductors, namely, niobium diselenide NbSe2 and iron selenide FeSe, and their intercalation compounds. Both NbSe2 and FeSe have received extensive scientific attention in recent years due to the coexistence of charge density waves, superconductivity and exotic pairing mechanisms at relatively high superconducting transition temperatures Tc. The intercalation of layered materials is known to tune their superconducting properties but an in depth understanding of superconductivity in these compounds remains lacking, partly because of a lack of high quality pure and single crystal samples on which to measure. In this work, a novel synthesis route is shown to create new single crystal forms of layered materials in order to achieve new high-quality superconductors. In the first part, NbSe2 is successfully intercalated with lithium to form LiNbSe2, a new superconductor with a Tc of 9.0 K, compared to 7.2 K for unintercalated NbSe2, confirmed by magnetometry and resistivity measurements. LiNbSe2 properties and structure are investigated with X-ray diffraction, Raman spectroscopy, magnetometry and resistivity, and DFT calculations. Upon intercalation phonons are found to have reduced energy due to an increase in the in-plane lattice parameters and shift of XRD 2θ values show the unit cell c-axis increases from 1.255(1) nm to 1.352(1) nm. The second part of the thesis investigates the superconductivity in FeSe and the intercalation compounds MXFe2Se2, where M is lithium, potassium or barium, and X is ammonia or methylamine. Metal intercalation is known to increase Tc from 8 K to 45 K. However, the mechanism is unknown not least because no one has successful intercalated single crystals required for many measurements. FeSe single crystals were synthesised using KCl/AlCl3 flux method. Single crystals were then successfully intercalated with metal via low temperature liquid ammonia and liquid methylamine method. The fabrication of FeSe and the intercalation using both condensed methods allow to discover new superconductors Li(NH3)Fe2Se2 (Tc = 30.5 K), K(NH3)Fe2Se2 (Tc = 30 K), K(CH3NH2)Fe2Se2 (Tc = 11.45 K), including record superconductor in these compounds of Tc at 47 K for Li(CH3NH2)Fe2Se2. These findings open up many new opportunities to realize FeSe-based pure and single phase superconductors with high Tc and to investigate the superconducting tuning in layered transition metals via dimensionality and doping, using scientific tools such as ARPES, STM and neutron scattering.

This thesis describes the measurement of the near-surface properties of organic semiconductors, and how these properties can be controllably modified, for use in future devices. Firstly however, a physical vapour transport organic single crystal growth system was built, and it was found that lower purity crystals (near-surface oxygen atomic content ~1 %) were more susceptible to oxidation than higher purity crystals (near-surface oxygen atomic content ~0.5 %). Steady-state photoluminescence spectra of the former show strong peaks sensitive to oxygen-related impurity presence. 6,6'-Dibromoindigo (Tyrian purple dye) single crystals were also grown and were, for the first time, characterised by atomic force microscopy and Raman spectroscopy. Nanopatterning of insulating oxide features on rubrene crystal surfaces was performed by local anodic oxidation, utilising an atomic force microscope tip. Oxide height increases with voltage bias and decreases with tip writing speed; 22 nm gaps at the surface between two parallel oxide lines were observed. Oxide depth was determined by conductance tomography, exposing subsurface layers without using chemical etching, whilst simultaneously mapping material conductance. Oxide depth exceeds its height; depth-to- height ratio is frequently above 1.6. Below an electric field of ~3×10⁶ V/cm oxide growth ceases, resulting in a maximum oxide vertical extent of ~60 nm at a voltage bias of ~20 V. Direct printing of 22 ± 3 μm wide electrical contacts on an organic semiconductor substrate was demonstrated, without requiring masking, lithography or surface treatment. Permanent photoconductivity reduction in rubrene two-terminal 'coplanar' devices was observed when devices were stored in ambient atmosphere after humidity exposure. Oxygen was localised near the surface. (75.2 ± 7.6) % of surface molecules are affected by oxygen incorporation and these may hinder exciton dissociation, correlated to the observed 60-90 % photocurrent reduction. Controllable mechanical scratching is used to study the flow of charge carriers in the near surface region of rubrene.

This thesis explores some of the fundamental properties of a rather special class of materials, the transparent conducting oxides. These 'semiconductors' combine the usually mutually exclusive properties of optical transparency with high electronic conductivity. Conventionally, TCOs are formed from metal-oxide structures doped with an element from the right hand column in the periodic table of either the anion (e.g. F in SnO2) or cation (Sn in In2O3). However, TCOs that use unconventional dopants (i.e. dopant elements not from the subsequent column in the periodic table) which display much improved optoelectronic properties are quite frequently reported in the literature. Most often, the host materials are doped with transition metal elements which can display unusual electronic configurations and many common oxidation states, making their properties as dopants hard to predict and understand. In this thesis, the properties of selected TCOs are presented in three case studies. The first study is on a conventionally doped and commercially available TCO, F:SnO2, in which the limitation of the electronic performance of the material is attributed to extrinsic defects associated with the dopant element. The second is a comparison between an In2O3 system doped with the transition metal Mo, and its conventionally doped and commercially relevant counterpart Sn:In2O3. In this study, the system with the novel dopant (Mo:In2O3) is shown to display much improved properties over the conventionally doped system. This is explained in the context of the band structure modifications due to choice of dopant. Finally, the surface properties of a relatively novel oxide semiconductor system, β-Ga2O3, are investigated. β-Ga2O3 has gained a lot of attention in the literature recently, and is a rare case of a III-VI oxide whose properties are not well established. The natural surface electronic state of this material is determined and the effect that surface H adsorption has on the surface space charge is investigated.

Accurately modelling charge trapping phenomena is a vital part of understanding and improving the behaviour of semiconductors in both current and future devices. While charge traps are frequently observed in doped crystals, the formation of socalled self-trapped polarons means that charges can trap even in defect-free bulk crystals. This in turn reduces charge carrier mobility in materials, sometimes to the detriment of the underlying device. More effective methods of modelling self-trapping typically introduce a few free parameters, each of which can significantly influence results obtained by the model. The focus of this thesis is on developing parameterfree, computationally inexpensive and accurate approaches to modelling charge trapping, with a focus on titanium dioxide, a material used in promising new photovoltaics. Through comparison to both experimental data and solutions to the exact many-electron Schr ̈odinger equation, this thesis demonstrates that use of the generalised Koopmans’ theorem in conjunction with hybrid functionals can yield strikingly accurate results. This technique is subsequently used to predict the formation of selftrapped charges in a number of titania phases, including the well-studied rutile and anatase, and less-known brookite, TiO2(H), TiO2(R) and TiO2(B). Intrinsic point defects are also investigated in rutile and anatase, where it is found that several interesting and unique electronic phenomena occur in their vicinity.

In this project some of the challenges of novel InSb based semiconducting material are investigated. Various features of electron transport in low dimensional semiconductors were studied for AlInSb/InSb quantum well (QW) two-dimensional electron gas (2DEG) heterostructures with an emphasis placed on realising onedimensional systems (which exhibit quantum phenomena where the conductance takes on a discrete 'step-like' nature). This material allows us to take advantage of very extreme material parameters such as light effective mass, the lowest binary material band gap, the highest electron mobility at room temperature, and an extremely large effective g-factor (with associated spin orbit coupling). However, this material still has significant challenges due to the large mismatch between the substrate GaAs and the QW, which produces threading dislocations that lead to limitations in mobility. Surface roughness has been investigated as a result of shallow etching for Ohmic contact deposition on the AlInSb/InSb wafer. Both dry and wet techniques have been investigated, and their effect on the electron transport as a function of roughness, primarily using Transmission Length Measurement (TLM). In addition, the Ohmic contact resistivity was investigated as a function of depth over a wide range of temperatures to extract an effective contact barrier. The contact potential barrier was found to have a strong effect at low temperatures, which leads to a non-linear I-V characteristic. Finally, this thesis studied different designs of nanoscale split gate structures that were fabricated on this state of the art InSb QW 2DEG material. This material was grown by collaborators at Sheffield University at the National Centre for III-V technologies. The devices were fabricated at Cardiff using photo-lithography and nanoscale electron beam lithography (EBL) using recipes tailored to this material.

This thesis details work investigating the oscillatory magnetoresistance (OMR) effect observed in superconducting nanowires. The OMR effect is a repeated rise and fall of resistance, in the otherwise monotonic magnetic field induced superconducting transition. Two material systems are studied: Nb nanowires, grown by DC sputter deposition, are used as a typical, commonly used superconductor; In-SnTe nanowires, synthesised by vapour transport growth, are used as a candidate topological superconductor. In-SnTe nanowires were grown without Au nanoparticles as a catalyst because, unexpectedly, the Au was observed to contaminate the crystal growth. The topological surface states are investigated through the observation of weak anti-localisation. Fitting to a 2D weak anti-localisation effect yields a maximum of four surface conductance channels, which is expected for this topological crystalline insulator. This thesis find that oscillatory magnetoresistance is a misnomer, the resistance modulation is not in the form of an oscillatory function. The OMR effect observed is closely described by a set of Gaussian distributions, centred at a series of magnetic fields. Several methods are used to probe the OMR effect, such as: alternating current, constant direct current and pulsed current-voltage. The relationship between the OMR effect is tested with relation to the temperature, applied current amplitude, frequency of the alternating current and the orientation of the applied magnetic field. Of the presently known candidates to describe an OMR effect, the most likely candidate is found to be periodic vortex motion. Vortex motion dissipates energy, causing a finite resistance. In this model, rates of vortex travel are modulated periodically with respect to an applied magnetic field. There are two main factors that contribute: the rearrangement of the vortex lattice at regular intervals in magnetic field; and the modulation of vortex entry and exit energy barriers. These two mechanisms combine to regularly inhibit vortex motion, reducing the resistance, and allow vortex motion, increasing the resistance. Pinning is found to dominate the characteristics of the OMR effect. This effect is more apparent in comparisons between the two types of nanowire grown. The mechanism behind the OMR effect appears to be due to the probabilistic motion of vortices. These motion events can be assisted by thermal energy or current flow. A new MHz frequency cut off in the OMR is observed, which can be attributed to the vortex dynamics.

Over the last decade, an 'iron age' of superconductivity has challenged the paradigm of unconventional pairing established by copper-oxide-based materials. Fascinatingly, in these iron-based compounds superconductivity emerges from a state in which electrons choose to distinguish between two equivalent directions of the underlying crystalline axes. The origin of this 'nematic' state is highly debated. This thesis concentrates on FeSe, a material appealing because its nematicity does not occur in proximity to long-range magnetic order. Although uniaxial strain couples to nematic order, experiments to date have focused on applying only a small symmetry-breaking strain. The mechanical properties of FeSe make utilising established piezoelectric-based apparatus, designed for continuous tuning of large uniaxial strains, challenging. In this thesis we develop a platform to which samples can be adhered, and apply large anisotropic strain to FeSe. When of the same symmetry as the nematicity, and larger than the structural distortion, this applied strain fully constrains the lattice. We provide a precise set of resistivity measurements across a wide temperature and strain range, revealing vital new phenomenologies. We establish the relationship between electrical transport and nematicity across a large strain range at the structural transition and, by isolating the influence of domain walls, characterise the elastoresistivity for temperatures below this transition. By tracking the onset of domain formation, we determine the temperature dependence of the spontaneous structural distortion, and use this to extract the intrinsic resistivity anisotropy within a single nematic domain. Interestingly, we discover a crossover at ~ 50 K between distinct high- and low-temperature behaviours. This thesis is also concerned with the development of apparatus for tuning strain. We conceptualise a new type of stress-controlled cell, which can apply large (up to 8 GPa in compression) uniaxial stresses to microstructured samples - pushing them to their ultimate mechanical limit.

In this thesis a Green's function based, analytical formalism is developed to describe dense chains of spiral ordered classical magnetic moments embedded in superconducting substrates. I demonstrate that an understanding of the dimensional mismatch between the substrate and impurity chain is crucial to understand the physics at play. Renormalised gap closures are discovered by exact, analytic solution for a ferromagnetic chain and insights gleaned are used to understand the spiral ordered case to which it can be smoothly tuned. I investigate the topological characteristics of this model and find an ambiguity in defining effective Hamiltonians due to the dimensional embedding of the chain in the substrate. To aid in resolving this ambiguity I develop formalism which allows one to write down Green's functions for bounded, semi infinite systems in terms of more easily attainable, exact solutions for infinite systems. I derive simple expressions to identify the presence of topological bound states which agrees with purely one dimensional models and changes suggestively when applied to the aforementioned two dimensional model. I then work to extend the formalism to allow the exact solution of two or three parallel chains, taking into account all possible interactions with the classical magnetic impurities. The solutions are decoupled so that they can be written in terms of the T matrices for a single chain, with additional levels of resummation. I find that the induced sub-gap spectrum for the two chain solution completely replaces those from each individual chain, leading to oscillating, helix like band structures. I use the complicated solution of the three chain solution to inform a potential ansatz to solve the N chain case.

We explore the roles of topology and time-reversal symmetry in one-dimensional superconducting systems. Specifically, we examine junctions involving time-reversal-invariant topological superconductors, which are characterised by the emergence of zero-energy Majorana- Kramers pairs at their boundaries. For Josephson junctions composed of these superconductors, we obtain, through a scattering matrix technique valid in a regime where the junction length is much shorter than the superconducting coherence length, exact analytical and numerical results for the Josephson current in terms of a small number of independently measurable junction parameters. The current is found to have a number of prominent and robust features which indicate the underlying symmetries and the nontrivial topology inherent in these systems. The most remarkable of these features occurs in the form of switches in the Josephson current, where the sign of the current reverses as a consequence of crossings between energy levels in the subgap spectrum. By utilising a quantum master equation approach, we establish general conditions under which these switches manifest in relation to a phenomenological relaxation rate and a voltage applied across the junction. Our findings enable quantitative predictions for such junctions, potentially assisting in experimental directions regarding the detection of Majorana- Kramers pairs in mesoscopic Josephson systems.

While the free electron model can often be surprisingly successful in describing properties of solids, there are plenty of materials in which interactions between electrons are too significant to be neglected. These strongly correlated systems sometimes exhibit rather unexpected, unusual and useful phenomena, understanding of which is one of the aims of condensed matter physics. Heat capacity measurements of paramagnetic YFe$_{2}$Ge$_{2}$ give a Sommerfeld coefficient of about 100 mJ mol$^{−1}$ K$^{−2}$, which is about an order of magnitude higher than the value predicted by band structure calculations. This suggests the existence of strong electronic correlations in the compound, potentially due to proximity to an antiferromagnetic quantum critical point (QCP). Existence of the latter is also indicated by the non-Fermi liquid T$^{3/2}$ behaviour of the low temperature resistivity. Below 1.8 K a superconducting phase develops in the material, making it a rare case of a non-pnictide and non-chalcogenide iron based superconductor with the 1-2-2 structure. This thesis describes growth and study of a new generation of high quality YFe$_{2}$Ge$_{2}$ samples with residual resistance ratios reaching 200. Measurements of resistivity, heat capacity and magnetic susceptibility confirm the intrinsic and bulk character of the superconductivity, which is also argued to be of an unconventional nature. In order to test the hypothesis of the nearby QCP, resistance measurements under high pressure of up to 35 kbar have been conducted. Pressure dependence of the critical temperature of the superconductivity has been found to be rather weak. μSR measurements have been performed, but provided limited information due to sample inhomogeneity resulting in a broad distribution of the critical temperature. While the superconductivity is the result of an effective attraction between electrons, under different circumstances the electronic properties of a system can instead be dictated by the Coulomb repulsion. This is the case for another transition metal based compound NiS$_{2}$, which is a Mott insulator. Applying hydrostatic pressure of about 30 kbar brings the material across the Mott metal-insulator transition (MIT) into the metallic phase. We have used the tunnel diode oscillator (TDO) technique to measure quantum oscillations in the metallised state of NiS$_{2}$, making it possible to track the evolution of the principal Fermi surface and the associated effective mass as a function of pressure. New results are presented which access a wider pressure range than previous studies and provide strong evidence that the effective carrier mass diverges close to the Mott MIT, as expected within the Brinkman-Rice scenario and predicted in dynamical mean field theory calculations. Quantum oscillations have been measured at pressures as close to the insulating phase as 33 kbar and as high as 97 kbar. In addition to providing a valuable insight into the mechanism of the Mott MIT, this study has also demonstrated the potential of the TDO technique for studying materials at high pressures.

Thermoelectric materials that can directly convert heat into electricity offer a possible avenue to address the world's increasing demand for energy. Metal-rich half-Heusler compounds are of interest due to their favourable electronic transport properties. Unfortunately, widespread application is limited by comparatively high thermal conductivity. The effect of processing and excess metal (Ni and Cu) on thermoelectric properties of MNiSn, M0.5M'0.5NiSn (M = Ti, Zr, Hf) and Ti0.5Zr0.25Hf0.25NiSn materials was investigated and is discussed in Chapters 3 and 4. This work revealed that Cu is effective n-type dopant, which improves electronic properties of half-Heusler materials. Detailed structure analysis, which included high-resolution synchrotron X-ray diffraction, neutron powder diffraction and electron microscopy revealed that most of the excess metals are randomly distributed on the interstitial sites, producing significant point defect scattering of phonons. In addition, Cu segregation leads to grain-by-grain compositional variations, with grains tending towards either half-Heusler or full-Heusler composition. In addition to the microstructural and properties studies, an in-situ neutron powder diffraction experiment was used to understand the formation of Ni-rich TiNi1+ySn (y = 0, 0.075 and 0.25) and multiphase M0.5M'0.5NiSn compositions during solid-state reaction. As described in Chapter 5, the half-Heusler formation occurs through a complex, multistep reaction, which involves many intermediates. ZrNiSn and Ti0.5Zr0.25Hf0.25NiSn underwent spontaneous self-propagating combustions, which is a new route to prepare impurity-free half-Heusler alloys. The last results Chapter describes the analysis of neutron total scattering data using Reverse Monte Carlo modelling. This study was performed to gain insight into spatial distribution of excess Ni within the half-Heusler structure. It confirmed random distribution of excess metal on the interstitial sites.

Superconducting quantum circuits have made tremendous advances in realizing engineered quantum dynamics for quantum simulation and quantum information processing over the past two decades. Technological developments in the field of superconducting circuits have raised them to be the leading platform for implementing many-qubit systems. This thesis introduces a sequence of concepts for engineering spin-lattice Hamiltonians in analog quantum simulation with superconducting circuits. Our approach to quantum simulation is to engineer driving schemes that lead to implementations of the desired models. The applications of this approach are in our work mainly centered around two types of systems: interesting many-body topological quantum systems, namely Kitaev's toric code and honeycomb model and two-body systems that can be employed as building blocks of larger quantum simulators or quantum computers. In the first part of this thesis, we make a proposal for an analog implementation of the toric code in superconducting circuits. We also discuss a realistic implementation of this model on an eight qubit lattice. In the second part, we present our analog approach for implementing arbitrary spinspin interactions in linearly and nonlinearly coupled superconducting qubits. Our proposed toolbox has the potential of easy generalization to a variety of systems and interactions. Lastly, based on our two-body toolbox, we set forward two possible implementations of the Kitaev honeycomb model and show that the engineered two-body interactions work - with good accuracy - in this many-body model.

The doping of organic semiconducting polymers was examined by studyingthe molecular vibrations through a combination of experimental spectroscopytechniques and the application of density functional theory (DFT) theoretical tools and the amplitude mode (AM) model. The IR spectra of the conjugated polymers P3HT, PFO and PCPDTBT were experimentally investigated. Particular focus was applied to PCPDTBT, where the effects of dopant electronegativity, dopant solvent choice and doping method were pursued. Doping induced vibrational modes in PCPDTBT were observed to have similar intensities to polaron absorption bands in the system. Comparisons to DFT calculations showed that these unusual intensity trends are the result of the molecular vibrations corresponding to the intense modes causing polaron displacement along the polymer backbone. Finally, a novel solution of the AM model was applied to the experimentally studied systems. The results of this suggest that PCPDTBT has the potential for higher carrier mobilities then P3HT.

This thesis describes the studies on the electronic structures of several novel quantum materials by using the Angle-Resolved Photoemission Spectroscopy (ARPES) technique:

1. Topological Dirac semimetals represent a new state of quantum matter that offers a platform for realizing many exotic physical phenomena. Our ARPES experiment systematically revealed the electronic structures of MSiS (M=Zr, Hf) family and confirmed the Dirac line-nodes states in both compounds. By comparing the spin-orbit coupling (SOC) effect, we demonstrated that the degeneracy of bands at certain positions of Brillouin zone (BZ) are protected by non-symmorphic symmetry of the crystal.
2. Two dimensional (2D) semiconductors with high carrier mobility and moderate band gap are particularly attractive for their potential broad applications in electronic devices. By using both ARPES and scanning tunneling microscopy (STM) techniques, we comprehensively revealed the electronic structure of newly discovered air-stable oxide semiconductor Bi2O2Se. Surface patterns (consisting of 50% Se vacancies) were found on the cleaved sample surface. Remarkably, we found no evidence of undesired in-gap states even in the presence of these surface defects.
3. Spatially resolved ARPES technique has been recently developed, which features its ability to focus the incident beam into submicron region. By using the technique, we studied the electronic structure of square graphene system. The sides of the graphene are found to be aligned with underlying Cu <110> direction, indicating the important role of substrate during the growth of graphene. In addition, large domain twisted bilayer graphene (tBLG) was artificially constructed. The van Hove singularity in its band structure caused by interlayer interaction was directly revealed by our ARPES measurement.

This thesis is concentrated on investigating the effect of the boundary conditions on p-wave superconductivity/superfluidity. The first part of the thesis discusses a possibility of creating a Josephson effect as a result of the geometry of the sample. The second part continues work on a theoretical investigation of 3He in a confined geometry. To approach these problems theoretically a Ginzburg-Landau theory of second order transitions was used, while for the second part a quasiclassical approach was established. For the first problem gap profiles for various opening angles were obtained allowing to build a final plot with Josephson current magnitude dependence on the configuration of the gap on the two sides of Josephson junction. For the second problem, self-consistent order parameter profiles and local densities of states were obtained for various spin-mixing angles. A value of the parameter that nullifies the confinement effect on 3He was found, allowing for B-phase to be stable in a slab. Also presented a discussion of other possible outcomes of magnetic scattering at the boundaries on spectral densities of states, such as stabilization of the polar phase and the extension of the zero energy states area of existence across the Fermi surface up to the equator of the sphere(p_z = 0).

A molecular junction consists of a single molecule or self-assembled monolayer (SAM) placed between two electrodes. It has varieties of functionalities due to quantum interference in nanoscale. Although there exist issues, advantages could still appeal to scientists who wish to investigate transport properties in many aspects such as electronics, thermoelectronics, spintronics, and optotronics. Recent studies of single-molecule thermoelectricity have identified families of high-performance molecules. However, controlled scalability might be used to boost electrical and thermoelectric performance over the current single-junction paradigm. In order to translate this discovery into practical thin-film energyharvesting devices, there is a need for an understanding of the fundamental issues arising when such junctions are placed in parallel. As a first step in this direction, we investigate here the properties of two C60 molecules placed in parallel and sandwiched between top and bottom graphene electrodes. It is found that increasing the number of parallel junctions from one to two can cause the electrical conductance to increase by more than a factor of 2 and furthermore, the Seebeck coefficient is sensitive to the number of parallel molecules sandwiched between the electrodes, whereas classically it should be unchanged. This non-classical behaviour of the electrical conductance and Seebeck coefficient are due to interjunction quantum interference, mediated by the electrodes, which leads to an enhanced response in these vertical molecular devices. Except the study of thermoelectricity, on the other hand, stable, single-molecule switches with high on-off ratios are an essential component for future molecularscale circuitry. Unfortunately, devices using gold electrodes are neither complementary metal-oxide-semiconductor (CMOS) compatible nor stable at room temperature. To overcome these limitations, several groups are developing electroburnt graphene electrodes for single molecule electronics. Here, in anticipation of these developments, we examine how the electrical switching properties of a series of porphyrin molecules with pendant dipoles can be tuned by systematically increasing the number of spacer units between the porphyrin core and graphene electrodes. The porphyrin is sandwiched between a graphene source and drain and gated by a third electrode. The associated rotation of porphyrin referred to graphene plane leads to the breaking of conjugation and a decrease in electrical conductances. As the number of spacers is increased, the conductance ratio can increase from 100 with one spacer to 200 with four spacers, and further enhanced by decreasing the temperature, reaching approximately 2200 at 100K. This design for a molecular switch using graphene electrodes could be extended to other aromatic systems. As mentioned in the design of 퐶60 -based thermoelectric vertical junction with graphene layers as electrodes and porphyrin-based switch in graphene nanogap, graphene provides a two-dimensional platform for contacting individual molecules, which enables transport spectroscopy of molecular orbital, spin, and vibrational states. Next, we report single-electron tunnelling through a molecule that has been anchored to two graphene leads. It is found that quantum interference within the graphene leads gives rise to an energy-dependent transmission and fluctuations in the sequential tunnelling. The lead states are electrostatically tuned by a global back-gate due to the weak screening effect compared to the metal electrodes, resulting in a distinct pattern of varying intensity in the measured conductance maps. This pattern could potentially obscure transport features that are intrinsic to the molecule under investigation. Finally, using ensemble averaged magneto-conductance measurements, lead and molecule states are disentangled, enabling spectroscopic investigation of the single molecule. As the above describes, there are varieties of research on the charge transport properties of molecular devices. It is noticed that noise exists in all electronic devices, and the investigation on noise could help us understand more fundamental information of the device, i.e. the imperfections and configurational changes in the system, the correlation of the transmission conduction channels or even exploit the noise characteristics for biosensing. In electroburnt graphene nanogaps, our collaborators observe that 1/f noise and random telegraph noise at room temperature and 77K respectively. Here, I employ a simple one-dimensional tight binding model to gauge the effect of two-level fluctuations in the electrostatic environment in the tunnel junctions. Two types of models are investigated. Model I describes the case that the environmental traps drive the tunnel barrier locally and differently. Model II is the case that the collective effect of all the environmental traps drives the tunnel barrier synchronously. It is concluded that the 77 K data is best described by a single environmental fluctuator influencing the transmission through the tunnel barrier. This may either occur via a local perturbation of the barrier potential, or via an overall modulation of the barrier height. A 1/푓 signal emerges as more fluctuators with different lifetime 휏 are added to the environment, corresponding to the thermal activation of multiple random telegraph noises (RTNs) at room temperature.

In this thesis we use a combination of density functional theory and equilibrium Green’s function to study thermoelectricity in molecular scale. We have aimed to improve the efficiency of single molecules in converting heat to electricity by carefully designing them. We introduced a novel strategy for designing molecules with low thermal conductance. This strategy states that adding side branches of different length to the backbone of a molecule can eliminate phonon transport through the backbone over a wide range of frequencies. Moreover, we demonstrate that chemical modification of thiophene molecular wire to ethylenedioxy-thiophene molecular wire can improve their thermoelectric efficiency. Furthermore, to demon- strate that the adopted molecular designs will be effective when scaled up to a self-assembled monolayer (SAM) of molecules, we model three independent exper- iments on gold-SAM-graphene vertical transport devices. The agreement between our calculations and the experiments elucidates the survival of quantum interfer- ence effect on a single molecular level in SAM devices. The work presented in this thesis has received considerable attention from many experimental groups in the UK and overseas stimulating novel experimental studies which are ongoing at present.

In this work, the optical properties of semiconductor materials were studied. Firstly, bismuth-containing silica thin film samples were measured that had been co-implanted with either Al or Si. Samples that underwent a rapid thermal annealing, did not exhibit the broadband NIR emission as expected. Rutherford backscattering spectroscopy found that Bi was being lost from the samples post-anneal, with the hottest anneals losing the most Bi and that higher concentrations of Al helped to retain more Bi. Lower temperature anneals exhibited a weak bismuth signal in samples with high Bi and Al implants, with the most pronounced signal at 700C 45 minute anneals. Temperature dependent pho- toluminescence (PL) of a bismuth-doped silicon oxynitride film showed that the emission was independent of the temperature. Secondly, various silicon nanocrystal (Si-nc) samples were studied. The optical gain of two samples with different sized Si-ncs was measured. It was found that the sample with the larger Si-ncs, exhibited a smaller gain and that this was due to this sample having a larger absorption. The gain of Si-nc samples with different concentrations of co-implanted erbium were also measured. For the Si-nc signal, a positive gain was measured for wave- lengths between 650-900nm. However, the sample with no Er exhibited a maximum gain of 13cm-1, with the maximum gain increasing to 32cm-1 for the 0.3x1016cm-2 Er sample, with a subsequent decrease in gain for an increase in the Er concentration. This is possibly due to the Si-ncs transferring energy to the Er centres. Gain measurements of the erbium signal of the sample containing 0.3x1016cm-2 of Er, found a large gain of 230cm-1, which again may be due to energy being transferred to the Er from Si-ncs. Time dependent gain taken of the sample with no Er found very little gain, that was independent of the time from the pump pulse. Lastly, InGaN/GaN multiple quantum well samples were measured. Power dependent gain measurements of sample GN1720 showed a reduction in the width of the positive gain band and a redshifting of the maximum gain with a reduction in pump intensity. For sample GN1717 only small differences in the gain were measured for wavelengths between 500-700nm. However, for both samples, the maximum gain was not seen at the maximum power and this may be due to higher free carrier absorption at this intensity. Power dependent PL, showed a large blueshift in emission for polar samples and a much reduced blueshift for semi-polar samples due to a reduced quantum confined stark effect (QCSE). The samples with a higher In content for each of the polar and semi-polar samples had the most blueshift due to more strain-induced QCSE. "Chevron" defect features, on sample GN2733, were studied via PL mapping and showed a 10nm redshift in emission and a reduction in intensity at the \join" of the chevron, possibly due to a higher In content here. A Raman map of the chevron showed an increase in frequency at the join for the A1 & E1 longitudinal optic (LO) mode. Polarised Raman mapping was conducted to try to measure the InGaN layer, the maps again exhibited a similar shift for the A1 & E1 mode at angles and polarisations where the intensity of this mode was high and low, indicating the scattering did not originate in the InGaN layer. As this shift was not seen at other modes it was attributed to LO phonon-plasmon coupling. IR resonant Raman measurements at the chevron join and away from it, showed no significant differences in their spectra.

Materials in proximity to quantum critical points (QCPs) experience strong fluctuations in the order parameter associated with the transition and often, as a result, display interesting properties. In this dissertation, we have used a variety of experimental probes such as Shubnikov-de Haas quantum oscillations, thermal conductivity and heat capacity, to better understand two such materials — $A_3T_4$Sn$_{13}$ and YFe$_2$Ge$_2$. $A_3T_4$Sn$_{13}$ ($A$ = Ca, Sr; $T$ = Ir, Rh) is a family of quasi-skutterudite superconductors with moderate $T_c$’s between 4 and 8 K. Although the superconductivity is believed to be phonon-mediated with s-wave pairing symmetry, an unusual second-order structural transition makes this material family fascinating to study. Whether this structural transition is a result of three distortions with perpendicular wavevectors resulting in a cubic-to-cubic transformation, or each wavevector acting independently giving rise to cubic-to-tetragonal transformations and formation of twinned domains is a disputed issue. We have measured quantum oscillations in the resistivity of Sr3Ir4Sn13 and compared it to density functional theory (DFT) calculations for both scenarios. Our results strongly suggest that the former interpretation is correct. The structural transition temperature $T^*$ in $A_3T_4$Sn$_{13}$ can be suppressed to zero by tuning with physical or chemical pressure. In (Ca$_x$Sr$_{1−x}$)$_3$Rh$_4$Sn$_13$, the quantum critical point can be accessed purely by chemical substitution at x ~ 0.9. In the vicinity of the QCP, we expect large fluctuations of the order parameter at low temperatures, which for a structural transition could manifest as a structural disorder. We have measured thermal conductivity at temperatures much lower than $T_c$ and found that it is well described by a single power law with suppressed exponents near the QCP. The heat capacity, however, remains ~ $T^3$. After excluding conventional phonon scattering mechanisms, we propose the possibility of intrinsic quasi-static spatial disorder that is related to the structural QCP. YFe$_2$Ge$_2$ is closely linked to the “122” family of iron-based superconductors like KFe$_2$As$_2$, although it has a significantly lower $T_c$ ~ 1 K. It has a rather three-dimensional Fermi surface which closely resembles that of KFe$_2$As$_2$ in the pressure-induced collapsed tetragonal phase. YFe$_2$Ge$_2$ is in proximity to several types of magnetic order which are predicted by DFT calculations to have lower energy than the non-spin polarised case. Even though YFe$_2$Ge$_2$ is non-magnetic, its superconductivity could be strongly affected by magnetic fluctuations. Through a collaboration with researchers at the University of Waterloo, we have measured the thermal conductivity of YFe$_2$Ge$_2$ down to millikelvin temperatures and up to 2.5 T in field. Our results suggest that YFe$_2$Ge$_2$ is a nodal superconductor. This result could assist in the explanation of the unconventional superconductivity in iron-based superconductors.