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An unresolved challenge facing electronics at a few-nm scale is that resistive channels start leaking due to quantum tunneling. This affects the performance of nanoscale transistors, with single-molecule devices displaying particularly low switching ratios and operating frequencies, combined with large subthreshold swings.1 The usual strategy to mitigate quantum effects has been to increase device complexity, but theory shows that if quantum effects are exploited correctly, they can simultaneously lower energy consumption and boost device performance.2-6 Here, we demonstrate experimentally how the performance of molecular transistors can be improved when the resistive channel contains two destructively-interfering waves. We use a zinc-porphyrin coupled to graphene electrodes in a three-terminal transistor device to demonstrate a >104 conductance-switching ratio, a subthreshold swing at the thermionic limit, a > 7 kHz operating frequency, and stability over >105 cycles. This performance is competitive with the best nanoelectronic transistors. We fully map the antiresonance interference features in conductance, reproduce the behaviour by density functional theory calculations, and trace back this high performance to the coupling between molecular orbitals and graphene edge states. These results demonstrate how the quantum nature of electron transmission at the nanoscale can enhance, rather than degrade, device performance, and highlight directions for future development of miniaturised electronics., Comment: 11 pages, 4 figures

Quantum interference in nano-electronic devices could lead to reduced-energy computing and efficient thermoelectric energy harvesting. When devices are shrunk down to the molecular level it is still unclear to what extent electron transmission is phase coherent, as molecules usually act as scattering centres, without the possibility of showing particle-wave duality. Here we show electron transmission remains phase coherent in molecular porphyrin nanoribbons, synthesized with perfectly defined geometry, connected to graphene electrodes. The device acts as a graphene Fabry-P\'erot interferometer, allowing direct probing of the transport mechanisms throughout several regimes, including the Kondo one. Electrostatic gating allows measurement of the molecular conductance in multiple molecular oxidation states, demonstrating a thousand-fold increase of the current by interference, and unravelling molecular and graphene transport pathways. These results demonstrate a platform for the use of interferometric effects in single-molecule junctions, opening up new avenues for studying quantum coherence in molecular electronic and spintronic devices., Comment: 14 pages, 3 figures

We study the quantum interference (QI) effects in three-terminal Andreev interferometers based on polyaromatic hydrocarbons (PAH's) under non-equilibrium conditions. The Andreev interferometer consists of a PAH coupled to two superconducting and one normal conducting terminals. We calculate the current measured in the normal lead as well as the current between the superconducting terminals under non-equilibrium conditions. We show that both the QI arising in the PAH cores and the bias voltage applied to a normal contact have a fundamental effect on the charge distribution associated with the Andreev Bound States (ABS's). QI can lead to a peculiar dependence of the normal current on the superconducting phase difference that was not observed in earlier studies of mesoscopic Andreev interferometers. We explain our results by an induced asymmetry in the spatial distribution of the electron- and hole-like quasiparticles. The non-equilibrium charge occupation induced in the central PAH core can result in a $\pi$ transition in the current-phase relation of the supercurrent for large enough applied bias voltage on the normal lead. The asymmetry in the spatial distribution of the electron- and hole-like quasiparticles might be used to split Cooper pairs and hence to produce entangled electrons in four terminal setups., Comment: 16 pages

The realization of self-assembled molecular-electronic films, whose room-temperature transport properties are controlled by quantum interference (QI), is an essential step in the scale-up QI effects from single molecules to parallel arrays of molecules. Recently, the effect of destructive QI (DQI) on the electrical conductance of self-assembled monolayers (SAMs) has been investigated. Here, through a combined experimental and theoretical investigation, we demonstrate chemical control of different forms of constructive QI (CQI) in cross-plane transport through SAMs and assess its influence on cross-plane thermoelectricity in SAMs. It is known that the electrical conductance of single molecules can be controlled in a deterministic manner, by chemically varying their connectivity to external electrodes. Here, by employing synthetic methodologies to vary the connectivity of terminal anchor groups around aromatic anthracene cores, and by forming SAMs of the resulting molecules, we clearly demonstrate that this signature of CQI can be translated into SAM-on-gold molecular films. We show that the conductance of vertical molecular junctions formed from anthracene-based molecules with two different connectivities differ by a factor of approximately 16, in agreement with theoretical predictions for their conductance ratio based on constructive QI effects within the core. We also demonstrate that for molecules with thiol anchor groups, the Seebeck coefficient of such films is connectivity dependent and with an appropriate choice of connectivity can be boosted by ~50%. This demonstration of QI and its influence on thermoelectricity in SAMs represents a critical step towards functional ultra-thin-film devices for future thermoelectric and molecular-scale electronics applications.

If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use 'magic number theory'. In contrast with counting rules and 'curly-arrow' descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores. Here we address the question of how conductance ratios are affected by electron-electron interactions. We find that due to cancellations of opposing trends, when Coulomb interactions and screening due to electrodes are switched on, conductance ratios are rather resilient. Consequently, qualitative trends in conductance ratios of molecules with extended pi systems can be predicted using simple 'non-interacting' magic number tables, without the need for large-scale computations. On the other hand, for certain connectivities, deviations from non-interacting conductance ratios can be significant and therefore such connectivities are of interest for probing the interplay between Coulomb interactions, connectivity and QI in single-molecule electron transport.

When a single molecule is connected to external electrodes by linker groups, the connectivity of the linkers to the molecular core can be controlled to atomic precision by appropriate chemical synthesis. Recently, the connectivity dependence of the electrical conductance and Seebeck coefficient of single molecules has been investigated both theoretically and experimentally. Here we study the connectivity dependence of the Wigner delay time of single-molecule junctions and the connectivity dependence of superconducting proximity effects, which occur when the external electrodes are replaced by superconductors. Although absolute values of transport properties depend on complex and often uncontrolled details of the coupling between the molecule and electrodes, we demonstrate that ratios of transport properties can be predicted using tables of 'magic numbers,' which capture the connectivity dependence of superconducting proximity effects and Wigner delay times within molecules. These numbers are calculated easily, without the need for large-scale computations. For normal-molecule-superconducting junctions, we find that the electrical conductance is proportional to the fourth power of their magic numbers, whereas for superconducting-molecule-superconducting junctions, the critical current is proportional to the square of their magic numbers. For more conventional normal-molecule-normal junctions, we demonstrate that delay time ratios can be obtained from products of magic number tables.

High electrical conductance molecular nanowires are highly desirable components for future molecular-scale circuitry, but typically molecular wires act as tunnel barriers and their conductance decays exponentially with length. Here we demonstrate that the conductance of fused-oligo-porphyrin nanowires can be either length independent or increase with length at room temperature. We show that this negative attenuation is an intrinsic property of fused-oligo-porphyrin nanowires, but its manifestation depends on the electrode material or anchor groups. This highly-desirable, non-classical behaviour signals the quantum nature of transport through such wires. It arises, because with increasing length, the tendency for electrical conductance to decay is compensated by a decrease in their HOMO-LUMO gap. Our study reveals the potential of these molecular wires as interconnects in future molecular-scale circuitry.

If the factors controlling the decay in single-molecule electrical conductance G with molecular length L could be understood and controlled, then this would be a significant step forward in the design of high-conductance molecular wires. For a wide variety of molecules conducting by phase coherent tunneling, conductance G decays with length following the relationship G = Aexp-\b{\eta}L. It is widely accepted that the attenuation coefficient \b{\eta} is determined by the position of the Fermi energy of the electrodes relative to the energy of frontier orbitals of the molecular bridge, whereas the terminal anchor groups which bind to the molecule to the electrodes contribute to the pre-exponential factor A. We examine this premise for several series of molecules which contain a central conjugated moiety (phenyl, viologen or {\alpha}-terthiophene) connected on either side to alkane chains of varying length, with each end terminated by thiol or thiomethyl anchor groups. In contrast with this expectation, we demonstrate both experimentally and theoretically that additional electronic states located on thiol anchor groups can significantly decrease the value of \b{eta}, by giving rise to resonances close to EF through coupling to the bridge moiety. This interplay between the gateway states and their coupling to a central conjugated moiety in the molecular bridges creates a new design strategy for realising higher-transmission molecular wires by taking advantage of the electrode-molecule interface properties.

Using a first principles approach combined with analysis of heuristic tight-binding models, we examine the connectivity dependence of two forms of quantum interference in single molecules. Based on general arguments, Fano resonances are shown to be insensitive to connectivity, while Mach-Zehnder-type interference features are shown to be connectivity dependent. This behaviour is found to occur in molecular wires containing anthraquinone units, in which the pendant carbonyl groups create Fano resonances, which coexist with multiple-path quantum interference features.

This overview will give a glimpse into chemical design principles for exploiting quantum interference (QI) effects in molecular-scale devices. Direct observation of room temperature QI in single-molecule junctions has stimulated growing interest in fabrication of tailor-made molecular electronic devices. Herein, we outline a new conceptual advance in the scientific understanding and technological know-how necessary to control QI effects in single molecules by chemical modification. We start by discussing QI from a chemical viewpoint and then describe a new magic ratio rule (MRR), which captures a minimal description of connectivity-driven charge transport and provides a useful starting point for chemists to design appropriate molecules for molecular electronics with desired functions. The MRR predicts conductance ratios, which are solely determined by QI within the core of polycyclic aromatic hydrocarbons (PAHs). The manifestations of QI and related quantum circuit rules for materials discovery are direct consequences of the key concepts of weak coupling, locality, connectivity, mid-gap transport and phase coherence in single-molecule junctions., Comment: Chemistry-A European Journal 2017

The thermoelectric figures of merit of pristine two-dimensional materials are predicted to be significantly less than unity, making them uncompetitive as thermoelectric materials. Here we elucidate a new strategy that overcomes this limitation by creating multi-layer nanoribbons of two different materials and allowing thermal and electrical currents to flow perpendicular to their planes. To demonstrate this enhancement of thermoelectric efficiency ZT, we analyse the thermoelectric performance of monolayer molybdenum disulphide (MoS2) sandwiched between two graphene monolayers and demonstrate that the cross-plane (CP) ZT is significantly enhanced compared with the pristine parent materials. For the parent monolayer of MoS2, we find that ZT can be as high as approximately 0.3, whereas monolayer graphene has a negligibly small ZT. In contrast for the graphene/MoS2/graphene heterostructure, we find that the CP ZT can be as large as 2.8. One contribution to this enhancement is a reduction of the thermal conductance of the van der Waals heterostructure compared with the parent materials, caused by a combination of boundary scattering at the MoS2/graphene interface which suppresses the phonons transmission and the lower Debye frequency of monolayer MoS2, which filters phonons from the monolayer graphene. A second contribution is an increase in the electrical conductance and Seebeck coefficient associated with molybdenum atoms at the edges of the nanoribbons.

We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry-Perot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry-Perot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

If design principles for controlling quantum interference in single molecules could be elucidated and verified, then this will lay the foundations for exploiting such effects in nanoscale devices and thin-film materials.When the core of a graphene-like polyaromatic hydrocarbon (PAH) is weakly coupled to external electrodes by atoms i and j, the single-molecule electrical conductance sigma-ij depends on the choice of connecting atoms i,j. Furthermore, conductance ratios sigma-ij/sigma-lm corresponding to different connectivities i,j and l,m are determined by quantum interference within the PAH core. In this paper, we examine how such conductance ratios change when one of the carbon atoms within the "parent" PAH core is replaced by a heteroatom to yield a "daughter" molecule. For bipartite parental cores, in which odd-numbered sites are connected to even-numbered sites only, the effect of heteroatom substitution onto an odd-numbered site is summarized by the following qualitative rules: (a) When i and j are odd, both parent and daughter have low conductances (b) When i is odd and j is even, or vice versa both parent and daughter have high conductances (c) When i,j are both even, the parent has a low conductance and the daughter a high conductance. These rules are verified by comparison with density-functional calculations on naphthalene, anthracene, pyrene and anthanthrene cores connected via two different anchor groups to gold electrodes.

We investigate the molecular sensing properties of carbon nanotube-boron nitride-carbon nanotube (CNT-BN-CNT) junctions. We demonstrate that the electrical conductance of such a junction changes in response to the binding of an analyte molecule to the region of BN. The change in conductance depends on the length of the BN spacer and the position of the analyte and therefore we propose a method of statistically analysing conductance data. We demonstrate the ability to discriminate between analytes, by computing the conductance changes due to three analytes (benzene, thiol-capped oligoyne and a pyridyl-capped oligoyne) binding to junctions with five different lengths of BN spacer.

A robust nanoelectromechanical switch is proposed based upon an asymmetric pendant moiety anchored to an organic backbone between two C60 fullerenes, which in turn are connected to gold electrodes. Ab initio density functional calculations are used to demonstrate that an electric field induces rotation of the pendant group, leading to a non-linear current-voltage relation. The non-linearity is strong enough to lead to negative differential resistance at modest source-drain voltages.

The solid-state structures of organic charge transfer (CT) salts are critical in determining their mode of charge transport, and hence their unusual electrical properties, which range from semiconducting through metallic to superconducting. In contrast, using both theory and experiment, we show here that the conductance of metal | single molecule | metal junctions involving aromatic donor moieties (dialkylterthiophene, dialkylbenzene) increase by over an order of magnitude upon formation of charge transfer (CT) complexes with tetracyanoethylene (TCNE). This enhancement occurs because CT complex formation creates a new resonance in the transmission function, close to the metal contact Fermi energy, that is a signal of room-temperature quantum interference.

Provided the electrical properties of electro-burnt graphene junctions can be understood and controlled, they have the potential to underpin the development of a wide range of future sub-10nm electrical devices. We examine both theoretically and experimentally the electrical conductance of electro-burnt graphene junctions at the last stages of nanogap formation. We account for the appearance of a counterintuitive increase in electrical conductance just before the gap forms. This is a manifestation of room-temperature quantum interference and arises from a combination of the semi-metallic band structure of graphene and a crossover from electrodes with multiple-path connectivity to single-path connectivity just prior to breaking. Therefore our results suggest that conductance enlargement prior to junction rupture is a signal of the formation of electro-burnt junctions, with a pico-scale current path formed from a single sp2-bond.

Molecular junctions are a versatile test bed for investigating thermoelectricity on the nanoscale1-10 and contribute to the design of new cost-effective environmentally-friendly organic thermoelectric materials11. It has been suggested that transport resonances associated with the discrete molecular levels would play a key role in the thermoelectric performance12,13, but no direct experimental evidence has been reported. Here we study single-molecule junctions of the endohedral fullerene Sc3N@C80 connected to gold electrodes using a scanning tunnelling microscope (STM). We find that the magnitude and sign of the thermopower depend strongly on the orientation of the molecule and on applied pressure. Our theoretical calculations show that the Sc3N inside the fullerene cage creates a sharp resonance near the Fermi level, whose energetic location and hence the thermopower can be tuned by applying pressure. These results reveal that Sc3N@C80 is a bi-thermoelectric material, exhibiting both positive and negative thermopower, and provide an unambiguous demonstration of the importance of transport resonances in molecular junctions.

Understanding phonon transport at a molecular scale is fundamental to the development of high-performance thermoelectric materials for the conversion of waste heat into electricity. We have studied phonon and electron transport in alkane and oligoyne chains of various lengths and find that due to the more rigid nature of the latter, the phonon thermal conductances of oligoynes are counter intuitively lower than that of the corresponding alkanes. The thermal conductance of oligoynes decreases monotonically with increasing length, whereas the thermal conductance of alkanes initially increases with length and then decreases. This difference in behaviour arises from phonon filtering by the gold electrodes and disappears when higher-Debye-frequency electrodes are used. Consequently a molecule that better transmits higher-frequency phonon modes, combined with a low-Debye-frequency electrode that filters high-energy phonons is a viable strategy for suppressing phonon transmission through the molecular junctions. The low thermal conductance of oligoynes, combined with their higher thermopower and higher electrical conductance lead to yield a maximum thermoelectric figure of merit of ZT = 1.4, which is several orders of magnitude higher than for alkanes.

We demonstrate how redox control of intra-molecular quantum interference in phase-coherent molecular wires can be used to enhance the thermopower (Seebeck coefficient) S and thermoelectric figure of merit ZT of single molecules attached to nanogap electrodes. Using first principles theory, we study the thermoelectric properties of a family of nine molecules, which consist of dithiol-terminated oligo(phenylene-ethynylenes) (OPEs) containing various central units. Uniquely, one molecule of this family possesses a conjugated acene-based central backbone attached via triple bonds to terminal sulfur atoms bound to gold electrodes and incorporates a fully conjugated hydroquinone central unit. We demonstrate that both S and the electronic contribution ZelT to the figure of merit ZT can be dramatically enhanced by oxidizing the hydroquinone to yield a second molecule, which possesses a cross-conjugated anthraquinone central unit. This enhancement originates from the conversion of the pi-conjugation in the former to cross-conjugation in the latter, which promotes the appearance of a sharp anti-resonance at the Fermi energy. Comparison with thermoelectric properties of the remaining seven conjugated molecules demonstrates that such large values of S and ZelT are unprecedented. We also evaluate the phonon contribution to the thermal conductance, which allows us to compute the full figure of merit ZT = ZelT/(1 + \k{appa}p/\k{appa}el), where \k{appa}p is the phonon contribution to the thermal conductance and \k{appa}el is the electronic contribution. For unstructured gold electrodes, \k{appa}p/\k{appa}el >> 1 and therefore strategies to reduce \k{appa}p are needed to realise the highest possible figure of merit.

Experiments using a mechanically-controlled break junction and calculations based on density functional theory demonstrate a new magic ratio rule (MRR),which captures the contribution of connectivity to the electrical conductance of graphene-like aromatic molecules. When one electrode is connected to a site i and the other is connected to a site i' of a particular molecule, we assign the molecule a magic integer Mii'. Two molecules with the same aromatic core, but different pairs of electrode connection sites (i,i' and j,j' respectively) possess different magic integers Mii' and Mjj'. Based on connectivity alone, we predict that when the coupling to electrodes is weak and the Fermi energy of the electrodes lies close to the centre of the HOMO-LUMO gap, the ratio of their conductances is equal to (Mii' /Mjj')2. The MRR is exact for a tight binding representation of a molecule and a qualitative guide for real molecules.

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers., Comment: in J. Am. Chem. Soc. (2015)

A quantum circuit rule for combining quantum interference (QI) effects in the conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules possessing three aromatic rings was investigated both experimentally and theoretically. Molecules were of the type X-Y-X, where X represents pyridyl anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a phenyl ring with p and m connectivities. The conductances GXmX (GXpX) of molecules of the form X-m-X (X-p-X), with meta (para) connections in the central ring were predominantly lower (higher), irrespective of the meta, para, or ortho nature of the anchor groups X, demonstrating that conductance is dominated by the nature of QI in the central ring Y. The single-molecule conductances were found to satisfy the quantum circuit rule Gppp/Gpmp = Gmpm/Gmmm. This demonstrates that the contribution to the conductance from the central ring is independent of the para versus meta nature of the anchor groups.

Self-heating is a severe problem for high-power microelectronic devices. Graphene and few-layer graphene have attracted tremendous attention for heat removal thanks to their extraordinarily high in-plane thermal conductivity. However, this high thermal conductivity undergoes severe degradations caused by the contact with the substrate and the functionalization-induced point defects. Here we show that thermal management of a micro heater can be substantially improved via introduction of alternative heat-escaping channels implemented with graphene-based film covalently bonded to functionalized graphene oxide through silane molecules. Theoretical and experimental results demonstrate a counter-intuitive enhancement of the thermal conductivity of such a graphene-based film. This increase in the in-plane thermal conductivity of supported graphene is accompanied by an improvement on the graphene-substrates thermal contact. Using infrared thermal imaging, we demonstrate that the temperature of the hotspots can be lowered by 12 $^o$C in transistors operating at 130 W mm$^{-2}$ , which corresponds to half of an order-of-magnitude increase in the device lifetime. Ab initio and molecular dynamics simulations reveal that the functionalization constrains the cross-plane scattering of low frequency phonons, which in turn enhances in-plane heat conduction of the bonded graphene film by recovering the long flexural phonon lifetime.

We demonstrate the potential of perylene bisimide (PBI) for label-free sensing of organic molecules by investigating the change in electronic properties of five symmetric and asymmetric PBI derivatives, which share a common backbone, but are functionalised with various bay-area substituents. Density functional theory was combined with a Greens function scattering approach to compute the electrical conductance of each molecule attached to two gold electrodes by pyridyl anchor groups. We studied the change in their conductance in response to the binding of three analytes, namely TNT, BEDT-TTF and TCNE, and found that the five different responses provided a unique fingerprint for the discriminating sensing of each analyte. This ability to sense and discriminate was a direct consequence of the extended {\pi} system of the PBI backbone, which strongly binds the analytes, combined with the different charge distribution of the five PBI derivatives, which leads to a unique electrical response to analyte binding., Comment: J. Mater. Chem. C, 2015

Devices formed from single molecules attached to noble-metal electrodes exhibit large conductance fluctuations, which inhibit their development as reproducible functional units. We demonstrate that single molecules with planar anchor groups attached to carbon-based electrodes are more resilient to atomic-scale variation in the contacts and exhibit significantly lower conductance fluctuations. We examine the conductance of a 2,6-dibenzylamino core-substituted naphthalenediimide chromophore attached to carbon electrodes by either phenanthrene anchors or more extended anchor groups, which include oligophenylene ethynylene spacers. We demonstrate that for the more spatially extended anchor groups conductance fluctuations are significantly reduced. The current-voltage characteristic arising from long-range tunneling is found to be strongly nonlinear with pronounced conductance suppression below a threshold voltage of approximately 2.5 V., Comment: 5 pages, 3 figures

We propose a DNA sequencing scheme based on silicene nanopores. Using first principles theory, we compute the electrical properties of such pores in the absence and presence of nucleobases. Within a two-terminal geometry, we analyze the current-voltage relation in the presence of nucleobases with various orientations. We demonstrate that when nucleobases pass through a pore, even after sampling over many orientations, changes in the electrical properties of the ribbon can be used to discriminate between bases.

Literature values for the energy gap of long one-dimensional carbon chains vary from as little as 0.2 eV to more than 4 eV. To resolve this discrepancy, we use the GW many-body approach to calculate the band gap $E_g$ of an infinite carbon chain. We also compute the energy dependence of the attenuation coefficient $\beta$ governing the decay with chain length of the electrical conductance of long chains and compare this with recent experimental measurements of the single-molecule conductance of end-capped carbon chains. For long chains, we find $E_g = 2.16$ eV and an upper bound for $\beta$ of $0.21$ \AA$^{-1}$., Comment: Accepted for publication in Journal of Chemical Physics

Using a first principles approach to electron transport, we calculate the electrical and thermoelectrical transport properties of a series of molecular wires containing benzo-difuran subunits. We demonstrate that the side groups introduce Fano resonances, the energy of which is changing with the electronegativity of selected atoms in it. We also study the relative effect of single, double or triple bonds along the molecular backbone and find that single bonds yield the highest thermopower, approximately 22$\mu$V/K at room temperature, which is comparable with the highest measured values for single-molecule thermopower reported to date., Comment: 7 pages, 8 figures

We propose an implementation of a valley selective electronic Veselago lens in bilayer graphene. We demonstrate that in the presence of an appropriately oriented potential step, low-energy electrons radiating from a point source can be re-focused coherently within the same band. The phenomenon is due to the trigonal warping of the band structure that leads to a negative refraction index. We show that the interference pattern can be controlled by an external mechanical strain., Comment: 14 pages, 8 figures

We implement a general method for correcting the low-bias transport properties of nanoscale systems within an ab-initio methodology based on linear combinations of atomic orbitals. We show how the typical problem of an underestimated HOMO-LUMO gap can be corrected, leading to quantitative and qualitative agreement with experiments. We show that an alternative method based on calculating the position of the relevant transport resonances and fitting them to Lorentzians can significantly underestimate the conductance and does not accurately reproduce the electron transmission coefficient between resonances. We compare this simple method in an ideal system of a benzene molecule coupled to featureless leads to more sophisticated approaches such as $GW$ and find a rather good agreement between both. We also present results for a benzene-dithiolate molecule between gold leads, where we study different coupling configurations for straight and tilted molecules, and show that this method yields the observed evolution of two-dimensional conductance histograms. We also explain the presence of low conductance zones in such histograms by taking into account different coupling configurations., Comment: 8 pages, 6 figures

The transport properties of a octane-dithiol (ODT) molecule coupled to Au(001) leads are analyzed using density functional theory and non-equilibrium Green functions. It is shown that a symmetric molecule can turn into a diode under influence of a local electric field created by an external charged probe. The origin of the asymmetry of the current--voltage ($I-V$) dependence is traced back to the appearance of a probe induced quasi--local state in the pseudogap of the ODT molecule. The induced state affects electron transport, provided it is close to the Fermi level of the leads. An asymmetric placement of the charged probe along the alkane chain makes the induced quasi--local state in the energy gap very sensitive to the bias voltage and results in rectification of the current. The results based on DFT are supported by independent calculations using a simple one--particle model Hamiltonian., Comment: 7 pages, 6 figures