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The deposition of a two-dimensional material on the surface of a three-dimensional crystal can generate superlattices with electronic properties modified through the proximity spin-orbit effect. In this study, we found that Kekul\'e graphene superlattices are obtained by placing graphene on Cd-terminated (001)-(1$\times$1) cadmium sulfide (CdS) surface. From an effective model of Kekul\'e superlattices, which is corroborated by Density Functional Theory (DFT) calculations, we identified that the puckered surfqace of CdS modifies the on-site energies (staggered potential) and C-C bonds, giving rise to two possible $\sqrt{3} \times \sqrt{3}$ hexagonal superlattices, which are known as Kekul\'e-O graphene and Kekul\'e-Y with a quadratic band crossing point. Both Kekul\'e superlattices present spin-orbit coupling due to the interaction of graphene with the CdS surface. To guide the experimental realization of Kekul\'e superlattices based on graphene/CdS heterostructures, we simulate electron diffraction patterns, as well as images from High-Resolution Transmission Electron Microscopy (HRTEM), and Scanning Transmission Electron Microscopy in the mode of High Angle Annular Dark Field (STEM-HAADF)., Comment: 9 pages, 4 figures

We investigate the electronic structure and transport properties of twisted bilayer graphene (TBLG) at a twist angle of $\theta\approx 1.696\text{{\deg}}$. Using a combination of molecular dynamics and tight-binding calculations, we find two superlattice gaps in the energy spectrum of the bulk, which emerge close to the Fermi level from the atomic rearrangement of the carbon atoms leading to a corrugation of the graphene sheets. Nanoribbons made from 1.696{\deg}-TBLG show edge-localized states inside the superlattice gaps. Applying the Green's function method, we demonstrate that the edge states carry electronic current with conductance values close to the conductance quantum. The edge states can generate a non-local resistance, which is not due to one-way transport at the edges but due to the fact that these states are localized only at certain edges of the system, depending on how the nanoribbon has been cut from the bulk., Comment: 9 pages, 6 figures

We study the electronic transport through uniformly bent carbon nanotubes. For this purpose, we describe the nanotube with the tight-binding model and calculate the local current flow by employing non-equilibrium Green's functions (NEGF) in the Keldysh formalism. In addition, we describe the low-energy excitations using an effective Dirac equation in curved space with a strain-induced pseudo-magnetic field which can be solved analytically for the torus geometry in terms of the Mathieu functions. We obtain a perfect quantitative agreement with the NEGF results. For nanotubes with an armchair edge, already a weak bending of 1% substantially changes the electronic properties. Depending on the valley, the current of the zero mode flows either on the outer or the inner side of the torus and, therefore, can be used as a valley splitter. In contrast, the zigzag nanotubes are largely unaffected by the bending. Our findings are of importance for nanoelectronic applications of carbon nanotubes and open new possibilities for valleytronics., Comment: 13 pages, 9 figures

We investigate the electronic transport in graphene nanoelectromechanical resonators (GrNEMS), known also as graphene nanodrums or nanomembranes. We demonstrate that these devices, despite small values of out-of-plane strain, between $0.1$ and $1\%$, can be used as efficient and robust valley polarizers and filters. Their working principle is based on the pseudomagnetic field generated by the strain of the graphene membrane. They work for ballistic electron beams as well as for strongly dispersed ones and can be also used as electron beam collimators due to the focusing effect of the pseudomagnetic field. We show additionally that the current flow can be estimated by semiclassical trajectories which represent a computationally efficient tool for predicting the functionality of the devices., Comment: 11 pages, 10 figures

We introduce a generalized Hamiltonian describing not only all topological phases observed experimentally in Kekul\'e graphene (KekGr) but predicting also new ones. These phases show features like a quadratic band crossing point, valley splitting, or the crossing of conduction bands, typically induced by Rashba spin-orbit interactions or Zeeman fields. The electrons in KekGr behave as Dirac fermions and follow pseudo-relativistic dispersion relations with Fermi velocities, rest masses, and valley-dependent self-gating. Transitions between the topological phases can be induced by tuning these parameters. The model is applied to study the current flow in KekGr $pn$ junctions evidencing a novel cooperative transport phenomenon, where Klein tunneling goes along with a valley flip. These junctions act as perfect filters and polarizers of massive Dirac fermions, which are the essential devices for valleytronics. The plethora of different topological phases in KekGr may also help to establish phenomena from spintronics., Comment: 7 pages, 5 figures

The effect of the Dirac cone tilt of anisotropic two-dimensional materials on the time evolution of coherent electron states in the presence of electric and magnetic fields is studied. We propose a canonical transformation that maps the anisotropic Dirac-Weyl Hamiltonian with tilted Dirac cones to an effective and isotropic Dirac Hamiltonian under these fields. In this way, the well-known Landau-level spectra and wave functions allow calculating the Wigner matrix representation of Landau and coherent states. We found a valley dependency in the behavior of the Wigner function for both Landau and coherent electron states. The time evolution shows that the interplay of the Dirac cone tilt and the electric field keeps the uncertainties of both position and momentum in one valley significantly lower than in the other valley. The increment of quantum noise correlates with the emergence of negative values in the Wigner function. These results may help us to understand the generation of coherent electron states under the interaction with electromagnetic fields. The reported valley-dependent signatures in the Wigner function of materials with tilted Dirac cones may be revealed by quantum tomography experiments, even in the absence of electric fields., Comment: 15 pages, 7 figures

A nanoelectronic device made of twisted bilayer graphene (TBLG) is proposed to steer the direction of the current flow. The ballistic electron current, injected at one edge of the bottom layer, can be guided predominantly to one of the lateral edges of the top layer. The current is steered to the opposite lateral edge, if either the twist angle is reversed or the electrons are injected in the valence band instead of the conduction band, making it possible to control the current flow by electric gates. When both graphene layers are aligned, the current passes straight through the system without changing its initial direction. The observed steering angle exceeds well the twist angle and emerges for a broad range of experimentally accessible parameters. It is explained by the trigonal shape of the energy bands beyond the van Hove singularity due to the Moir\'e interference pattern. As the shape of the energy bands depends on the valley degree of freedom, the steered current is partially valley polarized. Our findings show how to control and manipulate the current flow in TBLG. Technologically, they are of relevance for applications in twistronics and valleytronics., Comment: 10 pages, 10 figures

The interplay of strain engineering and photon-assisted tunneling of electrons in graphene is considered for giving rise to atypical transport phenomena. The combination of uniaxial strain and a time-periodic potential barrier helps to control the particle transmission for a wide range of tunable parameters. With the use of the tight-biding approach, the elasticity theory, and the Floquet scattering, we found an angular shift of the maximum transmission in the sidebands for uniaxial strains breaking the mirror symmetry with respect to the normal incidence, which is called anomalous Floquet tunneling. We show that electron tunneling depends strongly on the barrier width, incident angle, uniaxial strain, and the tuning of the time-periodic potential parameters. An adequate modulation of the barrier width and oscillation amplitude serves to select the transmission in the sidebands. These findings can be useful for controlling the electron current through the photon-assisted tunneling being used in multiple nanotechnological applications., Comment: 12 pages, 8 figures

We investigate the electron transport in smooth graphene pn junctions, generated by gradually varying electrostatic potentials. The numerically calculated coherent current flow patterns can be understood largely in terms of semi-classical trajectories, equivalent to the ones obtained for light beams in a medium with a gradually changing refractive index. In smooth junctions, energetically forbidden regions emerge, which increase reflections and can generate pronounced interference patterns, for example, whispering gallery modes. The investigated devices do not only demonstrate the feasibility of the gradient-index electron optics in graphene pn junctions, such as Luneburg and Maxwell lenses, but may have also technological applications, for example, as electron beam splitters, focusers and waveguides. The semi-classical trajectories offer an efficient tool to estimate the current flow paths in such nano-electronic devices., Comment: 11 pages, 15 figures

The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here with the aim of describing the effective disconnection of $\pi$ orbitals on these organic compounds. For periodic systems with time reversal symmetry, the emergent nodal domains are shown to divide the atomic chains into simpler carbon structures analog to benzene rings, diallyl chains, anthracene (triacene) chains and tetramethyl-naphtalene skeletal forms. The common electronic levels of these segments are identified as members of degenerate multiplets of the global system. The peculiar degeneracy of M\"obius cycloacene is also explained by segmentation. In the last part, it is shown that the multiplicity of energies for cycloacene can be foreseen by studying the continuous limit of the tight-binding model; the degeneracy conditions are put in terms of Chebyshev polynomials. The results obtained in this work have important consequences on the physics of electronic transport in organic wires, together with their artificial realizations., Comment: 19 pages, 17 figures

The current flow in phosphorene pnp junctions is studied. At the interfaces of the junction, omni-directional total reflection takes place, named anti-super-Klein tunneling, as this effect is not due to an energetically forbidden region but due to pseudo-spin blocking. The anti-super-Klein tunneling confines electrons within the junction, which thus represents a perfect lossless electron waveguide. Calculating the current flow by applying the Green's function method onto a tight-binding model of phosphorene, it is observed that narrow electron beams propagate in these waveguides like light beams in optical fibers. The perfect guiding is found for all steering angles of the electron beam as the total reflection does not rely on the existence of a critical angle. For low electron energies and narrow junctions, the guided modes of the waveguide are observed. The waveguide operates without any loss only for a specific orientation of the junction. For arbitrary orientations, minor leakage currents are found, which however decay for low electron energies and grazing incidence angles. It is shown that a crossroad shaped pnp junction can be used to split and direct the current flow in phosphorene. The proposed device, a phosphorene pnp junction as a lossless electron waveguide, may not only find applications in nanoelectronics but also in quantum information technology., Comment: 10 pages, 11 figures

The local current flow through three small aromatic carbon molecules, namely benzene, naphthalene and anthracene, is studied. Applying density functional theory and the non-equilibrium Green's function method for transport, we demonstrate that pronounced current vortices exist at certain electron energies for these molecules. The intensity of these circular currents, which appear not only at the anti-resonances of the transmission but also in vicinity of its maxima, can exceed the total current flowing through the molecular junction and generate considerable magnetic fields. The $\pi$ electron system of the molecular junctions is emulated experimentally by a network of macroscopic microwave resonators. The local current flows in these experiments confirm the existence of current vortices as a robust property of ring structures. The circular currents can be understood in terms of a simple nearest-neighbor tight-binding H\"uckel model. Current vortices are caused by the interplay of the complex eigenstates of the open system which have energies close-by the considered electron energy. Degeneracies, as observed in benzene and anthracene, can thus generate strong circular currents, but also non-degenerate systems like naphthalene exhibit current vortices. Small imperfections and perturbations can couple otherwise uncoupled states and induce circular currents.

We derive a continuity equation to study transport properties in a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a transport coefficient to characterize the efficiency of transport of each state. These quantities are studied explicitly using analytical expressions for the eigenvalues and eigenvectors of the system. We find that in states with broken $\mathcal{PT}$-symmetry, transport is inefficient, in the sense that either inflow exceeds outflow and density accumulates within the system, or outflow exceeds inflow, and the system becomes depleted. We also report the appearance of two subsets of interesting eigenstates whose eigenvalues are independent on the strength of the coupling to gain and loss. We call these opaque and transparent states. Opaque states are decoupled from the contacts and there is no transport; transparent states exhibit always efficient transport. Interestingly, the appearance of such eigenstates is connected with the divisors of the length of the system plus one and the position of the contacts. Thus the number of opaque and transparent states varies very irregularly., Comment: Major review and editing of the article based on ongoing revision process

Ballistic electrons in phosphorene $pn$ junctions show optical-like phenomena. Phosphorene is modeled by a tight-binding Hamiltonian that describes its electronic structure at low energies, where the electrons behave in the zigzag direction as massive Dirac fermions and in the orthogonal armchair direction as Schr\"odinger electrons. Applying the continuum approximation, we derive the electron optics laws in phosphorene $pn$ junctions, which show very particular and unusual properties. Due to the anisotropy of the electronic structure, these laws depend strongly on the orientation of the junction with respect to the sublattice. Negative and anomalous reflection are observed for tilted junctions, while the typical specular reflection is found only, if the junction is parallel to the zigzag or armchair edges. Moreover, omni-directional total reflection, called anti-super Klein tunneling, is observed if the junction is parallel to the armchair edge. Applying the nonequilibrium Green's function method on the tight-binding model, we calculate numerically the current flow. The good agreement of both approaches confirms the atypical transport properties, which can be used in nano-devices to collimate and filter the electron flow, or to switch its direction., Comment: 10 pages and 6 figures

Elastic deformations of graphene can significantly change the flow paths and valley polarization of the electric currents. We investigate these phenomena in graphene nanoribbons with localized out-of-plane deformations by means of tight-binding transport calculations. Such deformations can split the current into two beams of almost completely valley polarized electrons and give rise to a valley voltage. These properties are observed for a fairly wide set of experimentally accessible parameters. We propose a valleytronic nanodevice in which a high polarization of the electrons comes along with a high transmission making the device very efficient. In order to gain a better understanding of these effects, we also treat the system in the continuum limit in which the electronic excitations can be described by the Dirac equation coupled to curvature and a pseudo-magnetic field. Semiclassical trajectories offer then an additional insight into the balance of forces acting on the electrons and provide a convenient tool for predicting the behavior of the current flow paths. The proposed device can also be used for a sensitive measurement of graphene deformations., Comment: 9 pages, 9 figures

The robustness of quantum transport under various perturbations is analyzed in disordered interacting many-body systems, which are constructed from the embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE is perturbed with an ordinary EGE, the transport efficiency in the optimal cases is reduced significantly, while in the suboptimal cases the changes are less pronounced. Qualitatively the same behavior is observed, when parity and centrosymmetry are broken by block perturbations. Analyzing the influence of the environment coupling, optimal transport is observed at a certain coupling strength, while too weak and too strong coupling reduce the transport. Taking into account the effects of decoherence, in the EGE the transport efficiency approaches its maximum at a finite nonzero decoherence strength (environment-assisted transport). In the csEGE the efficiency decays monotonically with the decoherence but is always larger than in the EGE.

A new statistical model for the combined effects of decoherence, energy redistribution and dissipation on electron transport in large quantum systems is introduced. The essential idea is to consider the electron phase information to be lost only at randomly chosen regions with an average distance corresponding to the decoherence length. In these regions the electron's energy can be unchanged or redistributed within the electron system or dissipated to a heat bath. The different types of scattering and the decoherence leave distinct fingerprints in the energy distribution functions. They can be interpreted as a mixture of unthermalized and thermalized electrons. In the case of weak decoherence, the fraction of thermalized electrons show electrical and thermal contact resistances. In the regime of incoherent transport the proposed model is equivalent to a Boltzmann equation. The model is applied to experiments with carbon nanotubes. The excellent agreement of the model with the experimental data allows to determine the scattering lengths of the system., Comment: 19 pages, 11 figures

Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method., Comment: 7 pages, 5 figures, 1 table

The coherent transport of $n$ fermions in disordered networks of $l$ single-particle states connected by $k$-body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth as well as the ensemble-averaged total current attain their maximal values if the system is highly filled $n \sim l-1$ and $k\sim n/2$. For the cases $k=1$ and $k=n$ the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus, causes backscattering-free transmission resonances which enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for $n=l-1$, close to the highest observed currents., Comment: 14 pages, 15 figures

We study effects of different configurations of adsorbates on the vibrational modes as well as symmetries of polyacenes and poly-p-phenylenes focusing on lithium atom adsorption. We found that the spectra of the vibrational modes distinguish the different configurations. For more regular adsorption schemes the lowest states are bending and torsion modes of the skeleton, which are essentially followed by the adsorbate. On poly-p-phenylenes we found that lithium adsorption reduces and often eliminates the torsion between rings thus increasing symmetry. There is spontaneous symmetry breaking in poly-p-phenylenes due to double adsorption of lithium atoms on alternating rings., Comment: 5 pages, 6 figures

A novel approach to investigate the electron transport of cis- and trans-polyacetylene chains in the single-electron approximation is presented by using microwave emulation measurements and tight-binding calculations. In the emulation we take into account the different electronic couplings due to the double bonds leading to coupled dimer chains. The relative coupling constants are adjusted by DFT calculations. For sufficiently long chains a transport band gap is observed if the double bonds are present, whereas for identical couplings no band gap opens. The band gap can be observed also in relatively short chains, if additional edge atoms are absent, which cause strong resonance peaks within the band gap. The experimental results are in agreement with our tight-binding calculations using the nonequilibrium Green's function method. The tight-binding calculations show that it is crucial to include third nearest neighbor couplings to obtain the gap in the cis-polyacetylene., Comment: 6 pages, 8 figures

In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function (NEGF) method to the tight-binding model with local strain, b) the general relativistic approach in which classical trajectories of relativistic point particles moving in a curved surface with a pseudo-magnetic field are calculated. The connection between the two is established in the long-wave limit via an effective Dirac Hamiltonian in curved space. Geometrical optics approximation, applied to focused current beams, allows us to directly compare the wave and the particle pictures. We obtain very good numerical agreement between the quantum and the classical approaches for a fairly wide set of parameters, improving with the increasing size of the system. The presented method offers an enormous reduction of complexity from irregular tight-binding Hamiltonians defined on large lattices to geometric language for curved continuous surfaces. It facilitates a comfortable and efficient tool for predicting electronic transport properties in graphene nanostructures with complicated geometries. Combination of the curvature and the pseudo-magnetic field paves the way to new interesting transport phenomena such as bending or focusing (lensing) of currents depending on the shape of the deformation. It can be applied in designing ultrasensitive sensors or in nanoelectronics., Comment: 13 pages, 13 figures; added citations; added comments; typos corrected

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account., Comment: 13 pages, 12 figures

Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with their environment. We show that the decoherence distribution has observable effects on the transport. If the decoherence reservoirs are distributed randomly without spatial correlations, a minimal degree of decoherence is necessary to obtain Ohmic conduction. Below this threshold the system is localized and thus, a decoherence driven metal-insulator transition is found. In contrast, for homogenously distributed decoherence, any finite degree of decoherence is sufficient to destroy localization. Thus, the presence or absence of localization in a disordered one-dimensional system may give important insight about how the electron phase is randomized., Comment: 8 pages, 5 figures

We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field $B$ onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized 4-point Hall resistance $R_{xy}$ as a function of B. In weak fields, $R_{xy}$ shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, $R_{xy}$ shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in $B$ (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in $R_{xy}$. In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust., Comment: 7 pages, 8 figures

A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to describe the transport in an intermediate regime between classic and quantum transport. The model is based on B\"uttiker's approach using fictitious reservoirs for the dephasing effects. However, in contrast to other models, at the fictitious reservoirs complete phase randomization is assumed, which effectively divides the system into smaller coherent subsystems, and an ensemble average over randomly distributed dephasing reservoirs is calculated. This approach reduces not only the computation time but allows also to gain new insight into system properties. In this way, after deriving an efficient formula for the disorder-averaged resistance of a tight-binding chain, it is shown that the dephasing-driven transition from localized-exponentially to ohmic-linear behavior is not affected by the degree of momentum randomizing dephasing., Comment: 6 pages, 7 figures

True biaxial tests of granular materials are investigated by applying the principle of minimal dissipation and comparing to two dimensional contact dynamics simulations. It is shown that the macroscopic steady state manifested by constant stress ratio and constant volume is the result of the ever changing microscopic structure which minimizes the dissipation rate. The shear band angle in the varying shear band structures is found to be constant. We also show that introducing friction on the walls reduces the degeneracy of the optimal shear band structures to one for a wide range of parameters which gives a non-constant stress ratio curve with varying aspect ratio that can be calculated., Comment: 8 pages, 8 figures