We show that the wave functions form caustics in circular graphene p-n junctions which in the framework of geometrical optics can be interpreted with a negative refractive index.

A line defect on a metallic surface induces standing waves in the electronic local density of states (LDOS). Asymptotically far from the defect, the wave number of the LDOS oscillations at the Fermi energy is usually equal ...

We show that the charge conductivity for impurity-free multiband electronic systems can be expressed in terms of the nondiagonal elements of the Zitterbewegung amplitudes while the Berry curvature and the Chern number is ...

We study the electronic band structure of monolayer graphene when Rashba spin-orbit coupling is present. We show that if the Rashba spin-orbit coupling is stronger than the intrinsic spin-orbit coupling, the low-energy ...

We study theoretically the effect of spin-orbit coupling and sublattice asymmetry in graphene on the spin polarization of photoelectrons. We show that sublattice asymmetry in graphene not only opens a gap in the band ...

We study theoretically the coherent electron focusing in graphene nanoribbons. Using semiclassical and numerical tight-binding calculations we show that armchair edges give rise to equidistant peaks in the focusing spectrum. ...

We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson junctions. For low temperatures we find nonsinusoidal dependence of the supercurrent on the ...

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a 2×2 Hamiltonian. As an application we derive an analytical expression for the minimal conductivity ...

Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band ...

With a view to optimizing the design of carbon-nanotube (CNT) windmills and to maximizing the internal magnetic field generated by chiral currents, we present analytical results for the group-velocity components of an ...

We present a theoretical study of elastic spin-dependent electron scattering caused by a charged impurity in the vicinity of a two-dimensional electron gas. We find that the symmetry properties of the spin-dependent ...

We derive semiclassical quantization equations for graphene monolayer and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a ...

We studied the energy levels of graphene-based Andreev billiards consisting of a superconductor region on top of a monolayer graphene sheet. For the case of Andreev retroreflection we show that the graphene-based Andreev ...

We derive a general and simple expression for the time dependence of the position operator of a multiband Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasiparticle. Our result shows ...

We present a theoretical study of electron wave functions in ballistic circular n-p junctions of bilayer graphene. Similarly to the case of a circular n-p junction of monolayer graphene, we find that (i) the wave functions ...

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 ...

We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction (NPJ) in single and bilayer graphene. We compare the exact wave function inside the junction to that obtained from ...

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the ...

Results are presented for the electron current in gold chiral nanotubes (AuNTs). Starting from the band structure of (4,3) and (5,3) AuNTs, we find that the magnitude of the chiral currents are greater than those found in ...

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact ...

An experimental method for detection of bound states around an antidot formed from a hole in a graphene sheet is proposed by measuring the ballistic two terminal conductances. In particularly, we consider the effect of ...

To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The ...

The stability properties of the classical trajectories of charged particles are investigated in a two-dimensional inverse magnetic domain, where the magnetic field is zero inside the domain and constant outside. As an ...

We demonstrate that the exact quantum mechanical calculations are in good agreement with the semiclassical predictions for rectangular Andreev billiards, and therefore for a large number of open channels it is sufficient ...

The path-length spectra of mesoscopic systems including diffractive scatterers and connected to a superconductor are studied theoretically. We show that the spectra differ fundamentally from that of normal systems due to ...

The energy spectrum of cake shape normal-superconducting systems is calculated by solving the Bogoliubov-de Gennes equation. We take into account the mismatch in the effective masses and Fermi energies of the normal and ...

We present a detailed semiclassical study of a clean disk-shaped insulator-normal-metal-superconductor hybrid system in a magnetic field. It is based on an exact secular equation that we derived within the microscopic ...

Ballistic electrons confined to a billiard and subject to spin-orbit coupling of the Rashba-type are investigated, using both approximate semiclassical and exact quantum-mechanical methods. We focus on the low-energy part ...

A general expression for the Green's function of a system of N particles (bosons/fermions) interacting by contact potentials, including impurities with Dirac-delta-type potentials, is derived. In one dimension for N>2 ...

We study Andreev billiards of box and disk geometries by matching the wave functions at the interface of the normal and the superconducting region using the exact solutions of the Bogoliubov-de Gennes equation. The mismatch ...

Within the microscopic Bogoliubov-de Gennes formalism an exact quantization condition for Andreev bound states of the ferromagnetic-superconducting hybrid systems of box geometry is derived and a semiclassical formula for ...

Using a tight binding model we calculate the conductance of monovalent atomic chains for different contact geometries. The leads connected to the chains are modelled as semi-infinite fcc lattices with different orientations ...

The energy spectrum and the eigenstates of a rectangular quantum dot containing soft potential walls in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes equation. We compare the quantum ...

The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbours are represented by springs connecting them. A short and necessary introduction of the ...

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that the nonexact velocity reversal and the diffraction at the edges of the normal-superconductor contact ...

The resistance between arbitrary nodes of an infinite network of resistors is calculated when the network is perturbed by removing one bond from the perfect lattice. A relation is given between the resistance and the lattice ...

When two fully polarized ferromagnetic (F) wires with opposite polarizations make contact with a spin-singlet superconductor, a potential-induced current in wire 1 induces a non-local current of equal magnitude and sign ...

We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the ...

We propose a mixed analytical-ab initio method for the accurate calculation of the conductance in monovalent atomic wires. The method relies on the most general formula for ballistic transport through a monovalent wire, ...

We calculated the weak localization correction to the density of the transmission eigenvalues in the case of chaotic quantum dots in the framework of random matrix theory including the parametric dependence on the magnetic ...

Using the random matrix theory (RMT) approach, we calculated the weak localization correction to the shot noise power in a chaotic cavity as a function of magnetic field and spin-orbit coupling. We found a remarkably simple ...

We study the energy levels of non-interacting electrons confined to move in two-dimensional billiard regions and having a spin- dependent dynamics due to a finite Rashba spin splitting. The free space Green's function ...

We study the transport properties of a double quantum dot (DQD) molecule at zero and at finite temperature. The properties of the zero-temperature conductance depend on whether the level attraction between the symmetric ...

Comparing the results of exact quantum calculations and those obtained from the Einstein-Brillouin-Keller-like quantization scheme of Silvestrov [Phys. Rev. Lett. 90, 116801 (2003)] we show that the spectrum of Andreev ...

We present the generalization of the two-dimensional quantum scattering formalism to systems with Rashba spin-orbit coupling. Using symmetry considerations, we show that the differential scattering cross section depends ...

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength ...

The conductance of a waveguide containing a finite number of periodically placed identical pointlike impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities ...

We study a hybrid normal-superconductor (NS) pi junction in which the nonlocal current can be orders of magnitude larger than that in earlier proposed systems. We calculate the electronic transport of this NS hybrid system ...

We present a theoretical study of elastic spin-dependent electron scattering caused by a nonuniform Rashba spin-orbit coupling strength. Using the spin-generalized method of partial waves the complete scattering wave ...

The resistance between two arbitrary grid points of several infinite lattice structures of resistors is calculated by using lattice Green's functions. The resistance for d dimensional hypercubic, rectangular, triangular, ...

We present a unified treatment of Zitterbewegung phenomena for a wide class of systems including spintronic, graphene, and superconducting systems. We derive an explicit expression for the time dependence of the position ...