Peculiar Nature of Snake States in Graphene

We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to the two-dimensional electron gas (2DEG) snake states in graphene exibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated even if the Fermi energy lies between the first non-zero energy Landau levels of the conduction and valence bands. The nature of these states is studied by calculating the current density distribution. It is shown that besides the snake states in finite samples surface states also exist.Comment: 4 pages, 5 figure

Emergence of bound states in ballistic magnetotransport of graphene antidots

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 bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states. In addition, we develop a new numerical method in which the computational effort is proportional to the linear dimensions, instead of the area of the scattering region beeing typical for the existing numerical recursive Green's function method.Comment: 7 pages, 6 figure

Non-retracing orbits in Andreev billiards

The validity of the retracing approximation in the semiclassical quantization of Andreev billiards is investigated. The exact energy spectrum and the eigenstates of normal-conducting, ballistic quantum dots in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes equation and compared with the semiclassical Bohr-Sommerfeld quantization for periodic orbits which result from Andreev reflections. We find deviations that are due to the assumption of exact retracing electron-hole orbits rather than the semiclassical approximation, as a concurrently performed Einstein-Brillouin-Keller quantization demonstrates. We identify three different mechanisms producing non-retracing orbits which are directly identified through differences between electron and hole wave functions.Comment: 9 pages, 12 figures, Phys. Rev. B (in print), high resolution images available upon reques

Theory of resistor networks: The two-point resistance

The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte

Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

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 tensor of bilayer graphene as a function of a complex parameter w related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, and this directly affects the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on the Landauer approach, and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter w and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low-energy band structure

Human brain distinctiveness based on EEG spectral coherence connectivity

The use of EEG biometrics, for the purpose of automatic people recognition, has received increasing attention in the recent years. Most of current analysis rely on the extraction of features characterizing the activity of single brain regions, like power-spectrum estimates, thus neglecting possible temporal dependencies between the generated EEG signals. However, important physiological information can be extracted from the way different brain regions are functionally coupled. In this study, we propose a novel approach that fuses spectral coherencebased connectivity between different brain regions as a possibly viable biometric feature. The proposed approach is tested on a large dataset of subjects (N=108) during eyes-closed (EC) and eyes-open (EO) resting state conditions. The obtained recognition performances show that using brain connectivity leads to higher distinctiveness with respect to power-spectrum measurements, in both the experimental conditions. Notably, a 100% recognition accuracy is obtained in EC and EO when integrating functional connectivity between regions in the frontal lobe, while a lower 97.41% is obtained in EC (96.26% in EO) when fusing power spectrum information from centro-parietal regions. Taken together, these results suggest that functional connectivity patterns represent effective features for improving EEG-based biometric systems.Comment: Key words: EEG, Resting state, Biometrics, Spectral coherence, Match score fusio

Electronic standing waves on the surface of the topological insulator Bi2Te3

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 to the distance between nesting segments of the Fermi contour, and the envelope of the LDOS oscillations shows a power-law decay as moving away from the line defect. Here, we theoretically analyze the LDOS oscillations close to a line defect on the surface of the topological insulator Bi2Te3, and identify an important pre-asymptotic contribution with wave number and decay characteristics markedly different from the asymptotic contributions. Wave numbers characterizing the pre-asymptotic LDOS oscillations are in good agreement with recent data from scanning tunneling microscopy experiments [Phys. Rev. Lett. 104, 016401 (2010)].Comment: 8 pages, 5 figures; published versio

A simple model for the vibrational modes in honeycomb lattices

The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is presented. The dynamical matrix of the vibrational modes is then derived, and its eigenvalue problem is solved analytically. The solution may provide deeper insight into the nature of the vibrational modes. Numerical results for the vibrational frequencies are presented. To show that how effective our method used for the case of honeycomb lattice is, we also apply it to triangular and square lattice structures. A few suggested problems are listed in the concluding section.Comment: 9 pages, 12 figures, submitted to American Journal of Physic

Negative length orbits in normal-superconductor billiard systems

The Path-Length Spectra of mesoscopic systems including diffractive scatterers and connected to superconductor is studied theoretically. We show that the spectra differs fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path-lengths should arise in the spectra as opposed to normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the Path-Length Spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.Comment: 4 pages, 4 figures include