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The unusual observation of the Kondo effect in the two-dimensional electron gas (2DEG) of magnetically undoped AlGaN/GaN heterostructures is reported. The temperature-dependent zero-field resistivity data exhibits an upturn below 120 K, while the standard low-temperature weak localization and then weak antilocalization behaviour is revealed at T → 0. Magnetic transport investigations of the system are performed in the temperature range of 0.1–300 K and at magnetic fields up to 8 T, applied perpendicularly to the 2DEG plane. The experimental data are analyzed in terms of the multichannel Kondo model for d0 magnetic materials and weak localization theory taking into account the spin-orbit interaction.

The resistivity and magnetoresistance of multi-walled carbon nanotubes with different degrees of structural perfection in the temperature interval from 4.2 K to 293 K and in the magnetic field up t...

General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins. Limiting cases are obtained for one, two or three different kinds of spin occurring in a system. We show that a characteristic integer number Ns determines the formal form of spin quantum transport equations, irrespective of the type of spins or pseudospins, as well as the maximal entanglement entropy. The results may shed a new perspective on the mechanism leading to zero modes and chiral/helical edge states in topological insulators, integer quantum Hall effect topological insulator (QHE-TI), quantum spin Hall effect topological insulator (QSHE-TI) and Kondo topological insulator (Kondo-TI). It also shed new light in the observed competing weak localization and antilocalization in spin-dependent quantum transport measurements. In particular, a novel mechanism of localization and delocalization, as well as the new mechanism leading to the onset of superconductivity in bilayer systems seems to emerge naturally from torque entanglements in nonequilibrium quantum transport equations of spin and pseudospins. Moreover, the general results may serve as a foundation for engineering approximations of the quantum transport simulations of spintronic devices based on graphene and other 2-D materials such as the transition metal dichalcogenides (TMDs), silicene, as well as based on topological materials exhibiting quantum spin Hall effects. The extension of the formalism to spincaloritronics and pseudo-spincaloritronics is straightforward.

$\mathrm{Ca}{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ (CCRO) is considered a $d$-electron-based heavy-fermion metallic system with intriguing electronic properties. The magnetotransport measurements on metallic CCRO thin films reveal weak antilocalization (WAL) effects; however, it is not straightforward to infer whether the same originates from $e\text{\ensuremath{-}}e$ Coulomb interaction (EEI), spin-orbit interaction (SOI), or both present in CCRO. By evaluating quantum correction to sheet conductance for CCRO metallic thin films in the two-dimensional limit, it is observed that SOI gives rise to a dominant contribution to negative magnetoconductance (MC) in the weak-field regime. Based on weak localization (WL) and WAL analysis, SOI and inelastic scattering lengths (${l}_{so}$ and ${l}_{\ensuremath{\phi}}$) are obtained to be 30 and 74 nm, respectively, which indicates that WAL $({l}_{so}l{l}_{\ensuremath{\phi}})$ remains at play. The anisotropic effect of SOI is reflected in the field-direction-dependent in-plane and out-of-plane MC measurements. The presence of the EEI contribution is evidenced from (i) the linear increment (positive slope) of sheet conductance with $ln(T)$ in the quantum interference regime [only the WAL effect should otherwise show a negative slope with $ln(T)]$ and (ii) $ln(T)$ dependence of the Hall coefficient with a negative slope. Further, in the high-magnetic-field regime where WL or WAL is not valid, MC follows $ln(B)$-type behavior, indicating the presence of EEI. These findings have implications for the basic understanding of quantum magnetotransport properties in the presence of SOI and EEI in CCRO.

Van der Waals heterostructures composed of multiple few layer crystals allow the engineering of novel materials with predefined properties. As an example, coupling graphene weakly to materials with large spin–orbit coupling (SOC) allows to engineer a sizeable SOC in graphene via proximity effects. The strength of the proximity effect depends on the overlap of the atomic orbitals, therefore, changing the interlayer distance via hydrostatic pressure can be utilized to enhance the interlayer coupling between the layers. In this work, we report measurements on a graphene/WSe2 heterostructure exposed to increasing hydrostatic pressure. A clear transition from weak localization to weak antilocalization is visible as the pressure increases, demonstrating the increase of induced SOC in graphene.

We report the discovery of electric-field-induced transition from a topologically trivial to a topologically nontrivial band structure in an atomically sharp heterostructure of bilayer graphene (BLG) and single-layer WSe2 per the theoretical predictions of Gmitra and Fabian [Phys. Rev. Lett. 119, 146401 (2017)]. Through detailed studies of the quantum correction to the conductance in the BLG, we establish that the band-structure evolution arises from an interplay between proximity-induced strong spin-orbit interaction (SOI) and the layer polarizability in BLG. The low-energy carriers in the BLG experience an effective valley Zeeman SOI that is completely gate tunable to the extent that it can be switched on or off by applying a transverse displacement field or can be controllably transferred between the valence and the conduction band. We demonstrate that this results in the evolution from weak localization to weak antilocalization at a constant electronic density as the net displacement field is tuned from a positive to a negative value with a concomitant SOI-induced splitting of the low-energy bands of the BLG near the K (K') valley, which is a unique signature of the theoretically predicted spin-orbit valve effect. Our analysis shows that quantum correction to the Drude conductance in Dirac materials with strong induced SOI can only be explained satisfactorily by a theory that accounts for the SOI-induced spin splitting of the BLG low-energy bands. Our results demonstrate the potential for achieving highly tunable devices based on the valley Zeeman effect in dual-gated two-dimensional materials., 5 pages, 5 figures

Because of the one-dimensional confinement of electron momentum in narrow semiconductor wires, spin relaxation is suppressed irrespective of the presence of spin-orbit (SO) interaction. In quantum transport, weak localization corrections to conductivity are reflected as suppressed spin relaxation, which makes quantification of the SO strength difficult because quantum correction theory requires weak antilocalization when evaluating SO coefficients. Narrow wires with strong SO interaction are potential platform for Majorana particles and parafermions for topological electronics and quantum computation, so revealing the SO strength in semiconductor wire structures is beneficial. Herein, we present quantification of the full SO coefficient under weak localization in InGaAs-based narrow wires. Using anisotropic weak localization observed under an in-plane external magnetic field with various orientations, one can ascertain the relative ratio between Rashba ($\ensuremath{\alpha}$) and linear Dresselhaus (${\ensuremath{\beta}}_{1}$) SO coefficients with no fitting. Furthermore, we find that widely tuning the potential profile of the quantum well through the top gate can expose a Rashba-predominant region in magnetoconductance, where the $\ensuremath{\alpha}$ value can be extracted reliably from two-dimensional quantum correction theory. Finally, we quantify the full SO coefficients including Rashba, linear Dresselhaus, and cubic Dresselhaus terms in the wire.

Spin-orbit coupling (SOC) can provide essential tools to manipulate electron spins in two-dimensional materials like graphene, which is of great interest for both fundamental physics and spintronics application. In this paper, we report the low-field magnetotransport of in situ hydrogenated graphene where hydrogen atoms are attached to the graphene surface in continuous low temperature and vacuum environment. Transition from weak localization to weak antilocalization with increasing hydrogen adatom density is observed, indicating enhancing Bychkov-Rashba-type SOC in a mirror symmetry broken system. From the low-temperature saturation of phase breaking scattering rate, the existence of spin-flip scattering is identified, which corroborates the existence of magnetic moments in hydrogenated graphene.

Electron-electron interactions (EEIs) in 2D van der Waals (vdW) nanostructures is a topic of high current interest, with implications in both fundamental physics and nanoelectronics. In this Rapid Communication, we report the observation of a negative parabolic magnetoresistance (MR) in the multilayer 2D semiconductor InSe beyond the low-field weak localization/antilocalization regime, and provide evidence for the EEI origin of this MR behavior. Further, we analyze this negative parabolic MR and other observed quantum transport signatures of EEIs (temperature-dependent conductance and Hall coefficient) within the framework of Fermi-liquid theory and extract the gate voltage tunable Fermi-liquid parameter ${F}_{0}^{\ensuremath{\sigma}}$ which quantifies the electron spin-exchange interaction strength. This work opens up different directions for investigations of EEI effects in the electron transport of 2D vdW nanostructures.

The nodal-line semimetal is a new type of topological state of matter in which the crossing of two energy bands forms a nodal loop. In the absence of spin-orbit coupling, Mg3Bi2 is predicted as a type II nodal-line semimetal, which may evolve to a topological insulator with a small energy gap of ∼35 meV in the presence of spin-orbit coupling. However, the transport evidence is still lacking. Here, we measure the magneto-transport in Mg3Bi2. At low temperatures, the magnetoconductivity exhibits a weak antilocalization behavior. We fit the experimental data with a magnetoconductivity formula for the weak antilocalization effect of three-dimensional nodal-line semimetals as well as the well-known Hikami-Larkin-Nagaoka formula for two-dimensional weak (anti)localization effects. By comparing the fitting results of these two theories, we demonstrate that the weak antilocalization in Mg3Bi2 is better described by the theory for nodal-line semimetals. Our work will inspire more explorations to use the new weak localization theory to identify a large spectrum of nodal-line semimetals.

Quantum corrections to electrical resistance can serve as sensitive probes of the magnetic landscape of a material. For example, interference between time-reversed electron paths gives rise to weak localization effects, which can provide information about the coupling between spins and orbital motion, while the Kondo effect is sensitive to the presence of spin impurities. Here we use low-temperature magnetotransport measurements to reveal a transition from weak antilocalization (WAL) to Kondo scattering in the quasi-two-dimensional electron gas formed at the interface between SrTiO$_3$ and the Mott insulator NdTiO$_3$. This transition occurs as the thickness of the NdTiO$_3$ layer is increased. Analysis of the Kondo scattering and WAL points to the presence of atomic-scale magnetic impurities coexisting with extended magnetic regions that affect transport via a strong magnetic exchange interaction. This leads to distinct magnetoresistance behaviors that can serve as a sensitive probe of magnetic properties in two dimensions., 5 pages, 3 figures

Hall resistance $R_{\textrm{xy}}$ is commonly suggested to be linear-in-magnetic-field $B$, provided the field is small. We argue here that at low temperatures this linearity is broken due to weak localization/antilocalization phenomena in inhomogeneous systems, while in a uniform medium these effects do not affect the linear field dependence of $R_{\textrm{xy}}(B)$. We calculate the Hall resistance for different two-component media using a mean-field approach and show that this non-linearity is experimentally observable., 7 pages, 3 figures

We study theoretically weak localization of excitons in atomically-thin transition metal dichalcogenides. The constructive interference of excitonic de Broglie waves on the trajectories forming closed loops results in a decrease of the exciton diffusion coefficient. We calculate the interference contribution to the diffusion coefficient for the experimentally relevant situation of exciton scattering by acoustic phonons and static disorder. For the acoustic phonon scattering, the quantum interference becomes more and more important with increasing the temperature. Our estimates show that the quantum contribution to the diffusion coefficient is considerable for the state-of-the-art monolayer and bilayer transition metal dichalcogenides., Comment: 6 pages, 3 figures

As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling. However, the expansion breaks down at long times, and is not stabilized by including a mean-field decay rate, signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations and are relevant in two different contexts. First, in the search for precursors to many-body localization in the ergodic phase. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength, and provides an additional mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time., 31 pages, 29 figures; published version

We exploit the high-symmetry spin state obtained for equal Rashba and linear Dresselhaus interactions to derive a closed-form expression for the weak localization magnetoconductivity -- the paradigmatic signature of spin-orbit coupling in quantum transport. The small parameter of the theory is the deviation from the symmetry state introduced by the mismatch of the linear terms and by the cubic Dresselhaus term. In this regime, we perform quantum transport experiments in GaAs quantum wells. Top and back gates allow independent tuning of the Rashba and Dresselhaus terms in order to explore the broken-symmetry regime where the formula applies. We present a reliable two-step method to extract all parameters from fits to the new expression, obtaining excellent agreement with recent experiments. This provides experimental confirmation of the new theory, and advances spin-orbit coupling towards a powerful resource in emerging quantum technologies., 13 pages, 6 figures, supplementary included on arXiv

It is shown that the transport properties of graphitized silicon carbide are controlled by a surface graphene layer heavily doped with electrons. In weak magnetic fields and at low temperatures, a negative magnetoresistance is observed due to weak localization. A crossover in the magnetoresistance from weak localization to weak antilocalization (the latter is the manifestation of the isospin in graphene) is observed for the first time in samples of this kind at elevated temperatures. A pronounced pattern of Shubnikov–de Haas oscillations is observed in strong magnetic fields (up to 30 T). This pattern demonstrated fourfold carrier spectrum degeneracy due to the double spin and double valley degeneracies. Also, the manifestation of the Berry phase is observed. The effective electron mass is estimated to be m* = 0.08m0, which is characteristic of graphene with a high carrier concentration.

We have systematically investigated the disorder dependence electron phonon scattering rate in three dimensional disordered V82Pd18 − xFex alloys. A minimum in temperature dependence resistivity curve has been observed at low temperature T = T m . In the temperature range 5 K ≤ T ≤ T m the resistivity correction follows ρ o 5 / 2 T 1 / 2 law. The dephasing scattering time has been calculated from analysis of magnetoresistivity by weak localization theory. The electron dephasing time is dominated by electron–phonon scattering and follows anomalous temperature (T) and disorder ( ρ 0 ) dependence behaviour like τ e - ph − 1 ∝ T 2 / ρ 0 , where ρ 0 is the impurity resistivity. The magnitude of the saturated dephasing scattering time ( τ 0 ) at zero temperature decreases with increasing disorder of the samples. Such anomalous behaviour of dephasing scattering rate is still unresolved.

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS3 on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T0 ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T0. The negative magnetoresistance (at B ∥ c) below T0 is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.

Magnetotransport in heterostructures with spatial separation of the Mn magnetic impurity and an InGaAs quantum well is studied. An analysis of the observed effect of weak localization using the Hikami–Larkin–Nagaoki formula leads to an anomalously small value (0.4) of the prefactor. Obtained data indicate that inelastic e–e scattering can be the dominant dephasing mechanism in the structures under study. Analysis of the conductivity and magnetoresistance indicates the dominant role of spin-dependent scattering at fluctuations in the magnetic subsystem, which is consistent with an increase in the amplitude of the negative magnetoresistance and an increase in the Drude conductivity as a result of cooling. The nature of the anomalous Hall effect in the studied structures is investigated; in particular, indications are obtained that there is the presence of a topological contribution at low temperatures.

We consider the weak localization and the backscattering halo in media with strongly elongated scattering indicatrices. The earlier theory is generalized to the case of a nonuniform backscattering cross section in the rear hemisphere. Asymptotic formulas for the backscattering intensities are obtained in the low-angle diffusion approximation.

The Hall effect in heterostructures with a two-dimensional array of tunneling-coupled Ge quantum dots grown by molecular-beam epitaxy on Si is investigated. The conductivity of these structures in zero magnetic field at 4.2 K varies in the range of 10−12−10−4 Ω−1, which includes both the diffusive transport under weak localization conditions and hopping conduction. It is shown that the Hall effect can be discerned against the magnetoresistance-related background in both high- and low-conductivity structures. The Hall coefficient in the hopping regime exhibits a nonmonotonic dependence on the occupancy of quantum dots by holes. This behavior correlates with that of the localization length of the hole wavefunctions.

In this study, we develop a systematic weak localization/antilocalization theory fully considering the anisotropy and Berry phase of the system, and apply it to various phases of few-layer black phosphorus (BP), which has a highly anisotropic electronic structure with an electronic gap size tunable even to a negative value. The derivation of a Cooperon ansatz for the Bethe-Salpeter equation in a general anisotropic system is presented, revealing the existence of various quantum interference effects in different phases of few-layer BP, including a crossover from weak localization to antilocalization. We also predict that the magnetoconductivity at the semi-Dirac transition point will exhibit a nontrivial power-law dependence on the magnetic field, while following the conventional logarithmic field-dependence of 2D systems in the insulator and Dirac semimetal phases. Notably, the ratio between the magnetoconductivity and Boltzmann conductivity turns out to be independent of the direction, even in strongly anisotropic systems. Finally, we discuss the tunability of the quantum corrections of few-layer BP in terms of the symmetry class of the system., 16 pages, 4 figures

This thesis investigates electron transport properties in chemical vapor deposition (CVD) graphene-related nanostructures. There are many potential electronic and optoelectronic applications envisioned for graphene, due to its two-dimensional character and exceptional properties. However, the lack of scalability of exfoliated graphene and the high cost of epitaxial graphene on silicon carbide remain the major obstacles for further commercialization of graphene devices. Different approaches to solve this problem have been proposed for different applications and graphene grown by CVD stands out as a useful alternative and proves to be one of the viable routes towards scalable high quality electronics. This thesis presents a study of scalable nanostructured devices based on CVD graphene, with the purpose of understanding the quantum physics of electron transport and demonstrating the potential for nano-electronic applications. First, this thesis demonstrates a scalable approach towards encapsulating and passivating high quality CVD graphene field effect transistors (FETs), and electron scattering processes are explored by studying electrical characterisation and magnetotransport phenomena in encapsulated CVD AB stack and large twist angle (30◦) bilayer graphene FETs, as well as monolayer graphene FETs for reference. The result has significant impact on the widespread implementation of graphene for its scalable device applications. Second, in order to enhance spin-orbit coupling (SOC) in graphene for spin transport study and spintronics applications, a graphene - transition metal dichalcogenide (TMD) heterostructure is investigated. Phase coherence length is reduced in the heterostructure and a special transition from weak localization (WL) to weak antilocalization (WAL) is found around a certain carrier concentration due to surface roughness induced patches. This result provides insight into fabrication and operation of scalable graphene spintronic devices. Moreover, to further elucidate single-electron behaviours as well as solve the lack of bandgap issues, graphene is studied by being patterned into various quantum dot structures, such as nanoribbon multiple quantum dots, quantum Hall antidots, and double quantum dots (DQDs). The presence of multiple quantum dots in series is exhibited in a bilayer SiC epitaxial graphene nanoribbon, due to the interplay between disorder and quantum confinement. As an alternative to etched quantum dots in graphene, antidots in the quantum Hall regime can take advantage of Landau gaps in graphene and are explored via magnetotransport measurements at millikelvin temperature. Single-electron behaviors such as Aharonov-Bohm effect and Coulomb blockade effect are observed, whereas signatures of the effective antidots proved elusive, probably due to the disorder-broadening of the Landau levels. Finally, for the purpose of fast readout of charge and spin states, radio-frequency (RF) reflectometry technique is developed in GaAs antidots and graphene double quantum dots, corresponding to capacitive and resistive couplings to the devices respectively. This attempt paves a way for characterizing the time scale of the charge transfer and spin dephasing in graphene nanodevices. All the quantum dots studies in a scalable style lay the foundation for further quantum metrology and quantum computation applications. The research in this thesis enable us to better understand the quantum physics in CVD graphene, and the fabrication and operature of CVD graphene nanostructures are highly promising for future electronics.

We present magneto-transport study in an InAs/GaSb double quantum well structure in the weak localization regime. As the charge carriers are depleted using a top gate electrode, we observe a crossover from weak anti-localization (WAL) to weak localization (WL), when the inelastic phase breaking time decreases below spin-orbit characteristic time as a result of enhanced electron-electron interactions at lower carrier concentrations. The same crossover is observed with increasing temperature. The linear temperature behavior of inelastic scattering rate indicates that the dominant phase breaking mechanism in our 2D system is due to electron-electron interaction., 6 pages, 3 figures + Supplementary material (3 pages, 3 figures)

Non-linear to linear negative magnetoresistance (MR) was studied under the magnetic field ranging from &minus, 7 T to 7 T with a change in measurement temperature from 2 K to 300 K. Under the magnetic field of 7 T, a maximum MR magnitude of 8.2% was observed at 2 K. The chemical vapor deposition technique was adopted to synthesize the amorphous carbon thin films. Non-saturated and non-linear negative MR was observed for the lower temperatures, while 10 K was observed as transition temperature. Afterwards, the more likely linear MR behavior was observed up to 300 K. MR shape change was correlated with the structural morphology of metallic disordered graphitic layers or the random stacking of graphene layers with amorphous carbon. The negative MR mechanism for such a non-linear to linear shift was partially assumed as a combined effect of the diffused scattering theory and the weak localization theory. The negative MR effect has a direct relation with the degree of structural order.

Bilayer MoS2 is a centrosymmetric semiconductor with degenerate spin states in the six valleys at the corners of the Brillouin zone. It has been proposed that breaking of this inversion symmetry by an out-of-plane electric field breaks this degeneracy, allowing for spin and valley lifetimes to be manipulated electrically in bilayer MoS2 with an electric field. In this work, we report phase-coherent transport properties of double-gated mono-, bi-, and tri-layer MoS2. We observe a similar crossover from weak localization to weak anti-localization, from which we extract the spin relaxation time as a function of both electric field and temperature. We find that the spin relaxation time is inversely proportional to momentum relaxation time, indicating that D'yakonov-Perel mechanism is dominant in all devices despite its centrosymmetry. Further, we found no evidence of electric-field induced changes in spin-orbit coupling strength. This suggests that the interlayer coupling is sufficiently weak and that electron-doped dichalcogenide multilayers behave electrically as decoupled monolayers., Comment: 21 pages, 7 figures

Graphene is a promising material demonstrating some interesting phenomena such as the spin Hall effect, bipolar transistor effect, and non-trivial topological states. However, graphene has an intrinsically small spin–orbit interaction (SOI), making it difficult to apply in spintronic devices. The electronic band structure of graphene makes it possible to develop a systematic method to enhance SOI extrinsically. In this study, we designed a graphene field-effect transistor with a Pb layer intercalated between graphene (Gr) and Au layers and studied the effect on the strength of the SOI. The SOI in our system was significantly increased to 80 meV, which led to a giant non-local signal (∼180 Ω) at room temperature due to the spin Hall effect. Further, we extract key parameters of spin transport from the length and width dependence of non-local measurement. To support these findings, we also measured the temperature and gate-dependent weak localization (WL) effect. We obtained the magnitude of the SOI and spin relaxation time of Gr via quantitative analysis of WL. The SOI magnitudes estimated from the non-local signal and the WL effect are close in value. The enhancement of the SOI of Gr at room temperature is a potential simple manipulation method to explore the use of this material for spin-based applications.

At sufficiently low temperatures, many quantum effects, such as weak localization, electron-electron interaction (EEI), and Kondo screening, can lead to pronounced corrections to the semiclassical electron transport. Although low temperature corrections to longitudinal resistivity, ordinary Hall resistivity, or anomalous Hall (AH) resistivity are often observed, the corrections to three of them have never been simultaneously detected in a single sample. Here, we report on the observation of $\sqrt{T}$-type temperature dependences of the longitudinal, ordinary Hall and AH resistivities at temperatures down to at least 20 mK in $n$-type ${\mathrm{HgCr}}_{2}{\mathrm{Se}}_{4}$, a half-metallic ferromagnetic semiconductor that can reach extremely low carrier densities. For the samples with moderate disorder, the longitudinal and ordinary Hall conductivities can be satisfactorily described by the EEI theory developed by Altshuler et al., whereas the large corrections to AH conductivity are inconsistent with the existing theory, which predicts vanishing and finite corrections to AH conductivity for EEI and weak localization, respectively.

We derive a closed-form expression for the weak localization (WL) corrections to the magnetoconductivity of a 2D electron system with arbitrary Rashba $\alpha$ and Dresselhaus $\beta$ (linear) and $\beta_3$ (cubic) spin-orbit interaction couplings, in a perpendicular magnetic field geometry. In a system of reference with an in-plane $\hat{z}$ axis chosen as the high spin-symmetry direction at $\alpha = \beta$, we formulate a new algorithm to calculate the three independent contributions that lead to WL. The antilocalization is counterbalanced by the term associated with the spin-relaxation along $\hat{z}$, dependent only on $\alpha - \beta$. The other term is generated by two identical scattering modes characterized by spin-relaxation rates which are explicit functions of the orientation of the scattered momentum. Excellent agreement is found with data from GaAs quantum wells, where in particular our theory correctly captures the shift of the minima of the WL curves as a function of $\alpha/\beta$. This suggests that the anisotropy of the effective spin relaxation rates is fundamental to understanding the effect of the SO coupling in transport., Comment: 5 pages, 2 figures

Several cobalt-based Heusler alloys have been predicted to exhibit Weyl Semimetal behavior due to time reversal symmetry breaking. Co2TiGe is one of the predicted ferromagnetic Weyl semimetals. In this work, we report weak localization and small anomalous Hall conductivity in half-metallic Co2TiGe thin films grown by molecular beam epitaxy. The longitudinal resistivity shows semimetallic behavior. Elaborate analysis of longitudinal magnetoconductance shows the presence of a weak localization quantum correction present even up to room temperature and reduction in dephasing length at lower temperature. Negative longitudinal magnetoresistance is observed from 5 to 300 K, but at 300 K magnetoresistance becomes positive above 0.5 T magnetic field. The anomalous Hall effect has been investigated in these thin films. The measured anomalous Hall conductivity decreases with increasing temperature, and a small anomalous Hall conductivity has been measured at various temperatures which may be arising due to both intrinsic and extrinsic mechanisms.

New materials such as nodal-line semimetals offer a unique setting for novel transport phenomena. Here, we calculate the quantum correction to conductivity in a disordered nodal-line semimetal. The torus-shaped Fermi surface and encircled $\pi$ Berry flux carried by the nodal loop result in a fascinating interplay between the effective dimensionality of electron diffusion and band topology, which depends on the scattering range of the impurity potential relative to the size of the nodal loop. For a short-range impurity potential, backscattering is dominated by the interference paths that do not encircle the nodal loop, yielding a 3D weak localization effect. In contrast, for a long-range impurity potential, the electrons effectively diffuse in various 2D planes and the backscattering is dominated by the interference paths that encircle the nodal loop. The latter, leads to weak antilocalization with a 2D scaling law. Our results are consistent with symmetry consideration, where the two regimes correspond to the orthogonal and symplectic classes, respectively. Furthermore, we present weak-field magnetoconductivity calculations at low temperatures for realistic experimental parameters, and predict that clear scaling signatures $\propto\sqrt{B}$ and $\propto -\ln B$, respectively. The crossover between the 3D weak localization and 2D weak antilocalization can be probed by tuning the Fermi energy, giving a unique transport signature of the nodal-line semimetal., Comment: 19 pages, 4 figures, including supplemental material, the version to be published in PRL

Magnetoresistance in many samples of Dirac semimetal and topological insulator displays non-monotonic behaviors over a wide range of magnetic field. Here a formula of magnetoconductivity is presented for massless and massive Dirac fermions in Dirac materials due to quantum interference in scalar impurity scattering potentials. It reveals a striking crossover from positive to negative magnetoresistivity, uncovering strong competition between weak localization and weak antilocalization in multiple Cooperon modes at different chemical potentials, effective masses and finite temperatures. The work sheds light on the important role of strong coupling of the conduction and valence bands in the quantum interference transport in topological nontrivial and trivial Dirac materials., 6 pages, 3 figures

Theory of interference-induced quantum corrections to conductivity is developed for two dimensional systems with chiral spin textures including skyrmions. The effect of exchange interaction between electrons and spin textures on weak localization of electronic waves is studied. The spin dephasing rates are calculated as functions of the spin texture size. The anomalous magnetoresistance is shown to be governed by the size and magnetization spatial distribution of the spin textures. The effect of average magnetization-induced spin splitting on weak localization is analyzed. The sign-alternating weak-antilocalization magnetoresistance is demonstrated for skyrmion crystals. We argue that analysis of the low-field magnetoresistance serves as an independent tool for an experimental detection of chiral spin textures and, in particular, skyrmions., Comment: 6 pages, 4 Figures

A demonstration of 2D hole gases in GeSn/Ge heterostructures with a mobility as high as 20 000 cm2 V-1 s-1 is given. Both the Shubnikov-de Haas oscillations and integer quantum Hall effect are observed, indicating high sample quality. The Rashba spin-orbit coupling (SOC) is investigated via magneto-transport. Further, a transition from weak localization to weak anti-localization is observed, which shows the tunability of the SOC strength by gating. The magneto-transport data are fitted to the Hikami-Larkin-Nagaoka formula. The phase-coherence and spin-relaxation times, as well as spin-splitting energy and Rashba coefficient of the k-cubic term, are extracted. The analysis reveals that the effects of strain and confinement potential at a high fraction of Sn suppress the Rashba SOC caused by the GeSn/Ge heterostructures.

The low-temperature transport properties of titanium nitride wires with the width comparable with or much larger than the superconducting coherence length are studied experimentally. It is shown that the reduction of the width of wires does not affect the transport properties at the temperatures above the superconducting transition temperature and electron transport in this temperature range is determined by quantum contributions to the conductivity from weak localization and electron–electron interaction. It is established that the reduction of the width of wires does not change the superconducting transition temperature but completely suppresses the topological Berezinskii–Kosterlitz–Thouless transition. It is found that the threshold magnetic field increases with a decrease in the width of wires.

The sulfur passivation of the semi-insulating GaAs bulk (SI GaAs) grown in an excess phase of arsenic is used to observe the transition from the Coulomb blockade to the weak localization regime at room temperature. The I–V characteristics of the SI GaAs device reveal nonlinear behavior that appears to be evidence of the Coulomb blockade process as well as the Coulomb oscillations. The sulfur passivation of the SI GaAs device surface results in enormous transformation of the I–V characteristics that demonstrate the strong increase of the resistance and Coulomb blockade regime is replaced by the electron tunneling processes. The results obtained are analyzed within frameworks of disordering SI GaAs surface that is caused by inhomogeneous distribution of the donor and acceptor anti-site defects which affects the conditions of quantum- mechanical tunneling. Weak localization processes caused by the preservation of the Fermi level pinning are demonstrated by measuring the negative magnetoresistance in weak magnetic fields at room temperature. Finally, the studies of the magnetoresistance at higher magnetic fields reveal the h/2e Aharonov–Altshuler–Spivak oscillations with the complicated behavior due to possible statistical mismatch of the interference paths in the presence of different microdefects.

In present work a novel method for the functionalization of carbon nanotubes is proposed. The magnetoresistance of carbon nanotubes specimens in temperature range from 1.6 K up to 85 K and in magnetic field up to 5 T was investigated. It was shown that the proposed functionalization method does not cause any new defects in structure of carbon nanotubes and does not essentially influence the resistivity of nanotubes. It is revealed the appearance of the charge carriers weak localization and interactions effects for as-prepared and functionalized carbon nanotubes. On the basis of the experimental data, the explicit type of temperature dependence of wave function phase relaxation time and Fermi-level energy value for as-prepared and functionalized carbon nanotube are established.

We report experimental studies of conductance and magnetoconductance of GaAs/AlGaAs quantum well structures where both wells and barriers are doped by acceptor impurity Be. Temperature dependence of conductance demonstrate a non-monotonic behavior at temperatures around 100 K. At small temperatures (less than 10 K) we observed strong negative magnetoresistance at moderate magnetic field which crossed over to positive magnetoresistance at very strong magnetic fields and was completely suppressed with an increase of temperature. We ascribe these unusual features to effects of temperature and magnetic field on a degree of disorder. The temperature dependent disorder is related to charge redistribution between different localized states with an increase of temperature. The magnetic field dependent disorder is also related by charge redistribution between different centers, however in this case an important role is played by the doubly occupied states of the upper Hubbard band, their occupation being sensitive to magnetic field due to on-site spin correlations. The detailed theoretical model is present., 5 pages, 5 figures

Electrical transport property is closely related to the dimensionality of carriers' distribution. In this work, we succeed in tuning the carriers' distribution and the Rashba spin-orbit coupling at LaAlO3/SrTiO3 interface by varying the oxygen pressure (c-P O2) adopted in crystalline LaAlO3 growth. Measurements of the in-plane anisotropic magnetoresistance and the conducting-layer thickness indicate that the carriers' distribution changes from three to two dimensions with c-P O2 increasing, i.e. the electron confinement gets stronger. Importantly, by measuring the low-temperature out-of-plane magnetoresistance and analyzing the weak localization/weak anti-localization, we find that the strength of Rashba spin-orbit coupling can be enhanced by electron confinement. The electron confinement is a manifestation of breaking of spatial inversion symmetry. Therefore, our work reveals the intimate relationship between spatial inversion symmetry breaking and Rashba spin-orbit coupling at the LaAlO3/SrTiO3 interface, and provides a new method to tune the Rashba spin-orbit coupling, which is valuable in the application of oxide-spintronics.

Transport signatures of exchange gap opening because of magnetic proximity effect (MPE) are reported for bilayer structures of Bi2Se3 thin films on yttrium iron garnet (YIG) and thulium iron garnet (TmIG) of perpendicular magnetic anisotropy (PMA). Pronounced negative magnetoresistance (MR) was detected, and attributed to an emergent weak localization (WL) effect superimposing on a weak antilocalization (WAL). Thickness-dependent study shows that the WL originates from the time-reversal-symmetry breaking of topological surface states by interfacial exchange coupling. The weight of WL declined when the interfacial magnetization was aligned toward the in-plane direction, which is understood as the effect of tuning the exchange gap size by varying the perpendicular magnetization component. Importantly, magnetotransport study revealed anomalous Hall effect (AHE) of square loops and anisotropic magnetoresistance (AMR) characteristic, typifying a ferromagnetic conductor in Bi2Se3/TmIG, and the presence of an interfacial ferromagnetism driven by MPE. Coexistence of MPE-induced ferromagnetism and the finite exchange gap provides an opportunity of realizing zero magnetic-field dissipation-less transport in topological insulator/ferromagnetic insulator heterostructures., 31 pages, 9 figures

Studying the influence of broken time-reversal symmetry on topological materials is an important fundamental problem of current interest in condensed matter physics and its understanding could also provide a route toward proof-of-concept spintronic devices that exploit spin-textured topological states. Here we develop a new model quantum material for studying the effect of breaking time-reversal symmetry: a hybrid heterostructure wherein a ferromagnetic semiconductor Ga1−xMnxAs, with an out-of-plane component of magnetization, is cleanly interfaced with a topological insulator (Bi,Sb)2(Te,Se)3 by molecular beam epitaxy. Lateral electrical transport in this bilayer is dominated by conduction through (Bi,Sb)2(Te,Se)3 whose conductivity is a few orders of magnitude higher than that of highly resistive Ga1−xMnxAs. Electrical transport measurements in a top-gated heterostructure device reveal a crossover from weak antilocalization to weak localization as the temperature is lowered or as the chemical potential approaches the Dirac point. This is accompanied by a systematic emergence of an anomalous Hall effect. These results are interpreted in terms of the opening of a gap at the Dirac point due to exchange coupling between the topological insulator surface state and the ferromagnetic ordering in Ga1−xMnxAs. The experiments described here show that well-developed III–V ferromagnetic semiconductors could serve as valuable components of artificially designed quantum materials aimed at exploring the interplay between magnetism and topological phenomena. A carefully engineered device allows the study of the role of time-reversal symmetry breaking in topological insulators. The topological properties and surface states of materials like bismuth selenide are protected by time-reversal symmetry, so it is crucial to understand how phenomena like ferromagnetism that break this symmetry will affect these states. Joon Sue Lee and collaborators from the Pennsylvania State University have created a device consisting of a topological insulator thin film grown on top of a ferromagnetic layer with tightly controlled doping in both layers. Quantum transport measurements show that the exchange interactions from the ferromagnet create a gap in the surface states at the interface while the far surface of the topological insulator remains gapless. Similar devices will enable detailed study of the fundamental role of symmetries in topological materials.

Since the discovery of graphene, the localization physics has been studied extensively, and both weak antilocalization (WAL) and weak localization (WL) have been observed. A graphene superlattice (GSL) with multiple Dirac cones has emerged as a focus point in condensed-matter physics in recent years. However, the localization physics at multiple Dirac cones has not been studied to date. Here, we study the magnetoconductance in hexagonal boron nitride-graphene moir\'e-superlattice devices. Our magnetoconductance results show a clear signature of WL at the cloned Dirac cone (CDC) over one decade of variation of both carrier concentration and temperature in the two devices. In contrast, the WAL becomes stronger at the primary Dirac cone (PDC) with increasing temperature and lower carrier concentration in one device, in agreement with previous studies, whereas the other device shows stronger WAL for both lower temperature and carrier concentration. Since the observation of WAL at PDC is expected in a cleaner device due to the $\ensuremath{\pi}$ Berry phase, it is natural to ask whether the observation of WL at CDC in our GSL devices has any connection to Berry phase change or not. In order to address this issue we measure the Shubnikov--de Haas (SdH) resistance oscillations, which show a shift of the Berry phase by $\ensuremath{\pi}$ from PDC to CDC, indicating the role of the Berry phase for observing WL at CDC. We further corroborate our results with realistic electronic band structure calculations, which suggest a change in the Fermi surface topology from that with a small Fermi pocket enclosing a single PDC in each valley to a large Fermi surface shared by all the CDCs, in accordance with the change in oscillation frequency from PDC to CDC in the SdH measurements.

The persistent spin helix (PSH) state in III--V semiconductor quantum wells (QWs) is a promising candidate for spin-based applications because the PSH state realizes controllable spin orientation with long spin lifetime. Although the cubic Dresselhaus spin-orbit (SO) interaction is known for breaking the PSH state in both (001)-oriented and (110)-oriented QWs, it is not well understood how the distinct symmetry of cubic Dresselhaus terms ${\ensuremath{\beta}}_{3}$ between (001) and (110) QWs affects the robustness of the PSH state. Here we investigate robustness of the PSH state between (001) and (110) QWs under various strengths of cubic Dresselhaus SO interaction based on numerical Monte Carlo approach and magnetoconductance simulation, respectively, representing optical spin excitation/detection and weak localization/weak antilocalization in magnetotransport. For electron spins initialized along $z\ensuremath{\parallel}[001]$ in a (001) QW and $x\ensuremath{\parallel}[001]\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}y\ensuremath{\parallel}[1\overline{1}0]$ in a (110) QW, where the spin distribution is developed with the helical spin mode, a (001) QW shows a more robust PSH state against the increase of ${\ensuremath{\beta}}_{3}$ than does a (110) QW. This phenomenon is contrary to numerically computed magnetoconductance, where weak localization is maintained on the variation of ${\ensuremath{\beta}}_{3}$ in a (110) QW, whereas weak antilocalization appears in a (001) QW. By deriving the spin lifetime of the PSH state in a (110) QW from a diffusion equation using a random-walk approach, we demonstrate that such a difference arises directly from the magnitude and orientation of third angular harmonics in cubic Dresselhaus fields for (001) and (110) QWs.

Two-dimensional conducting interfaces in ${\mathrm{SrTiO}}_{3}$-based heterostructures display a variety of coexisting and competing physical phenomena, which can be tuned by the application of a gate voltage. (111) oriented heterostructures have recently gained attention due to the possibility of finding exotic physics in these systems due to their hexagonal surface crystal symmetry. In this work, we use magnetoresistance to study the evolution of spin-orbit interaction and magnetism in (111) oriented (${\mathrm{La}}_{0.3}{\mathrm{Sr}}_{0.7})({\mathrm{Al}}_{0.65}{\mathrm{Ta}}_{0.35}){\mathrm{O}}_{3}/{\mathrm{SrTiO}}_{3}$. At more positive values of the gate voltage, which correspond to high carrier densities, we find that transport is multiband, and dominated by high-mobility carriers with a tendency toward weak localization. At more negative gate voltages, the carrier density is reduced, the high-mobility bands are depopulated, and weak antilocalization effects begin to dominate, indicating that spin-orbit interaction becomes stronger. At millikelvin temperatures, at gate voltages corresponding to the strong spin-orbit regime, we observe hysteresis in magnetoresistance, indicative of ferromagnetism in the system. Our results suggest that in the (111) (${\mathrm{La}}_{0.3}{\mathrm{Sr}}_{0.7})({\mathrm{Al}}_{0.65}{\mathrm{Ta}}_{0.35}){\mathrm{O}}_{3}/{\mathrm{SrTiO}}_{3}$ system, low-mobility carriers that experience strong spin-orbit interactions participate in creating magnetic order in the system.

Manipulating the electron spin with the aid of spin-orbit coupling (SOC) is an indispensable element of spintronics. Electrostatically gating a material with strong SOC results in an effective magnetic field which can in turn be used to govern the electron spin. In this work, we report the existence and electrostatic tunability of Rashba SOC in multilayer InSe. We observed a gate-voltage-tuned crossover from weak localization (WL) to weak antilocalization (WAL) effect in quantum transport studies of InSe, which suggests an increasing SOC strength. Quantitative analyses of magneto-transport studies and energy band diagram calculations provide strong evidence for the predominance of Rashba SOC in electrostatically gated InSe. Furthermore, we attribute the tendency of the SOC strength to saturate at high gate voltages to the increased electronic density of states-induced saturation of the electric field experienced by the electrons in the InSe layer. This explanation of nonlinear gate voltage control of Rashba SOC can be generalized to other electrostatically gated semiconductor nanomaterials in which a similar tendency of spin-orbit length saturation was observed (e.g. nanowire field effect transistors), and is thus of broad implications in spintronics. Identifying and controlling the Rashba SOC in InSe may serve pivotally in devising III-VI semiconductor-based spintronic devices in the future., 7 pages, 5 figures

We report an approach for examining electron properties using information about the shape and size of a nanostructure as a measurement reference. This approach quantifies the spin precession angles per unit length directly by considering the time-reversal interferences on chaotic return trajectories within mesoscopic ring arrays (MRAs). Experimentally, we fabricated MRAs using nanolithography in InGaAs quantum wells which had a gate-controllable spin-orbit interaction (SOI). As a result, we observed an Onsager symmetry related to relativistic magnetic fields, which provided us with indispensable information for the semiclassical billiard ball simulation. Our simulations, developed based on the real-space formalism of the weak localization/antilocalization effect including the degree of freedom for electronic spin, reproduced the experimental magnetoconductivity (MC) curves with high fidelity. The values of five distinct electron parameters (Fermi wavelength, spin precession angles per unit length for two different SOIs, impurity scattering length, and phase coherence length) were thereby extracted from a single MC curve. The methodology developed here is applicable to wide ranges of nanomaterials and devices, providing a diagnostic tool for exotic properties of two-dimensional electron systems.

Topological qubits based on Majorana Fermions have the potential to revolutionize the emerging field of quantum computing by making information processing significantly more robust to decoherence. Nanowires are a promising medium for hosting these kinds of qubits, though branched nanowires are needed to perform qubit manipulations. Here we report a gold-free templated growth of III–V nanowires by molecular beam epitaxy using an approach that enables patternable and highly regular branched nanowire arrays on a far greater scale than what has been reported thus far. Our approach relies on the lattice-mismatched growth of InAs on top of defect-free GaAs nanomembranes yielding laterally oriented, low-defect InAs and InGaAs nanowires whose shapes are determined by surface and strain energy minimization. By controlling nanomembrane width and growth time, we demonstrate the formation of compositionally graded nanowires with cross-sections less than 50 nm. Scaling the nanowires below 20 nm leads to the formation of homogeneous InGaAs nanowires, which exhibit phase-coherent, quasi-1D quantum transport as shown by magnetoconductance measurements. These results are an important advance toward scalable topological quantum computing., Authors from EPFL and U. Basel acknowledge funding through the NCCR QSIT. Authors from EPFL further thank funding from SNF (project no. IZLRZ2-163861) and H2020 via the ITN project INDEED. Work at U. Basel was partially supported by the Swiss NSF, and the Swiss Nanoscience Institute SNI. S.M.S. acknowledges funding from “Programa Internacional de Becas “la Caixa″-Severo Ochoa”. J.A. and S.M.S. acknowledge funding from Generalitat de Catalunya 2017 SGR 327 and the Spanish MINECO coordinated project ValPEC (ENE2017-85087-C3). ICN2 acknowledges support from the Severo Ochoa Programme (MINECO, grant no. SEV2013-0295) and is funded by the CERCA Programme/Generalitat de Catalunya. This work has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 654360 NFFA-Europe. V.G.D. thanks the Ministry of Education and Science of the Russian Federation for financial support under grant no. 14-613-21-0055 (project ID RFMEFI61316 × 0055). L.J.L. acknowledges support of NSF DMR-1611341. M.O.H. acknowledges support of the NSF GRFP. NUCAPT received support from the MRSEC program (NSF DMR-1720139) at the Materials Research Center, the SHyNE Resource (NSF ECCS-1542205), and the Initiative for Sustainability and Energy (ISEN) at Northwestern University.

Confinement and edge structures are known to play significant roles in electronic and transport properties of two-dimensional materials. Here, we report on low-temperature magnetotransport measurements of lithographically patterned graphene cavity nanodevices. It is found that the evolution of the low-field magnetoconductance characteristics with varying carrier density exhibits different behaviors in graphene cavity and bulk graphene devices. In the graphene cavity devices, we have observed that intravalley scattering becomes dominant as the Fermi level gets close to the Dirac point. We associate this enhanced intravalley scattering to the effect of charge inhomogeneities and edge disorder in the confined graphene nanostructures. We have also observed that the dephasing rate of carriers in the cavity devices follows a parabolic temperature dependence, indicating that the direct Coulomb interaction scattering mechanism governs the dephasing at low temperatures. Our results demonstrate the importance of confinement in carrier transport in graphene nanostructure devices., Comment: 13 pages, 5 figures

We observe an unusual behavior of the low-temperature magnetoresistance of the high-mobility two-dimensional electron gas in InGaAs/InAlAs quantum wells in weak perpendicular magnetic fields. The observed magnetoresistance is qualitatively similar to that expected for the weak localization and anti-localization but its quantity exceeds significantly the scale of the quantum corrections. The calculations show that the obtained data can be explained by the classical effects in electron motion along the open orbits in a quasiperiodic potential relief manifested by the presence of ridges on the quantum well surface.

Semiconductor Bi$_2$O$_2$Se nanolayers of high crystal quality have been realized via epitaxial growth. These two-dimensional (2D) materials possess excellent electron transport properties with potential application in nanoelectronics. It is also strongly expected that the 2D Bi$_2$O$_2$Se nanolayers could be of an excellent material platform for developing spintronic and topological quantum devices, if the presence of strong spin-orbit interaction in the 2D materials can be experimentally demonstrated. Here, we report on experimental determination of the strength of spin-orbit interaction in Bi$_2$O$_2$Se nanoplates through magnetotransport measurements. The nanoplates are epitaxially grown by chemical vapor deposition and the magnetotransport measurements are performed at low temperatures. The measured magnetoconductance exhibits a crossover behavior from weak antilocalization to weak localization at low magnetic fields with increasing temperature or decreasing back gate voltage. We have analyzed this transition behavior of the magnetoconductance based on an interference theory which describes the quantum correction to the magnetoconductance of a 2D system in the presence of spin-orbit interaction. Dephasing length and spin relaxation length are extracted from the magnetoconductance measurements. Comparing to other semiconductor nanostructures, the extracted relatively short spin relaxation length of ~150 nm indicates the existence of strong spin-orbit interaction in Bi$_2$O$_2$Se nanolayers., Comment: 14 pages, 4 figures, and 5 pages of Supplementary Materials