Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems

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 operator of the quasiparticles which can be decomposed into a mean part and an oscillatory term. The latter corresponds to the Zitterbewegung. To apply our result for different systems one needs to use only vector algebra instead of the more complicated operator algebra.Comment: 4 pages, 1 table, v2 is slightly revise

Relation between Zitterbewegung and the charge conductivity, Berry curvature and the Chern number of multi band systems

We show that the charge conductivity for impurity free multi band electronic systems can be expressed in terms of the diagonal and non-diagonal elements of the Zitterbewegung amplitudes while the Berry curvature and the Chern number is related only to the diagonal elements. Thus, the phenomenon of the Zitterbewegung can no longer be viewed just as an interesting consequence of quantum physics but it has also an experimental relevance. Moreover, through several examples we demonstrate how efficient our approach is in the analytical calculation of the charge conductivity.Comment: 4 pages and a littl

Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors

We calculate the resistance between two arbitrary grid points of several infinite lattice structures of resistors by using lattice Green's functions. The resistance for $d$ dimensional hypercubic, rectangular, triangular and honeycomb lattices of resistors is discussed in detail. We give recurrence formulas for the resistance between arbitrary lattice points of the square lattice. For large separation between nodes we calculate the asymptotic form of the resistance for a square lattice and the finite limiting value of the resistance for a simple cubic lattice. We point out the relation between the resistance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. Our Green's function method can be applied in a straightforward manner to other types of lattice structures and can be useful didactically for introducing many concepts used in condensed matter physics

Electronic and spin properties of Rashba billiards

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 of the spectrum that has negative eigenvalues. When the spin precession length is smaller than the radius of the billiard, the low--lying energy eigenvalues turn out to be well described semiclassically. Corresponding eigenspinors are found to have a finite spin polarization in the direction perpendicular to the billiard plane.Comment: 5 pages, 2 figure

Josephson current in ballistic superconductor-graphene systems

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 superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviaton of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed by a diffusive or ballistic metal. The relation to other recent theoretical results on graphene Josephson junctions is pointed out and the possible experimental relevance of our work is considered as well

Perturbation of infinite networks of resistors

The resistance between arbitrary nodes of infinite networks of resistors is studied when the network is perturbed by removing one bond from the perfect lattice. A connection is made between the resistance and the lattice Green's function of the perturbed network. Solving Dyson's equation the Green's function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results are presented for a square lattice. Our method of the lattice Green's function in studying resistor networks can also be applied in the field of random walks as well as electrical and mechanical breakdown phenomena in insulators, thin films and modern ceramics.Comment: 10 pages, 4 figures, submitted to American Journal of Physic

Differential scattering cross section of the non-Abelian Aharonov-Bohm effect in multiband systems

We develop a unified treatment of the non-Abelian Aharonov-Bohm (AB) effect in isotropic multiband systems, namely, the scattering of particles on a gauge field corresponding to a noncommutative Lie group. We present a complex contour integral representation of the scattering states for such systems, and, using their asymptotic form, we calculate the differential scattering cross section. The angular dependence of the cross section turns out to be the same as that obtained originally by Aharonov and Bohm in their seminal paper, but this time it depends on the polarization of the incoming plane wave. As an application of our theory, we perform the contour integrals for the wave functions explicitly and calculate the corresponding cross section for three non-trivial isotropic multiband systems relevant to condensed matter and particle physics. To have a deeper insight into the nature of the scattering, we plot the probability and current distributions for different incoming waves. This paper is a generalization of our recent results on the Abelian AB effect providing an extension of exactly solvable AB scattering problems.Comment: 10 pages, 5 figure

Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures

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 transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the quantum anomalous Hall state placed on the top of dielectric multilayers. The optical conductivity of the bilayer graphene is calculated in the framework of a four-band model.Comment: 10 pages, 6 figure

Rashba billiards

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 Green's function for such Rashba billiards is constructed analytically and used to find the area and perimeter contributions to the density of states, as well as the smooth counting function. We show that, in contrast to systems with spin-rotational invariance, Rashba billiards always possess a negative energy spectrum. A semi-classical analysis is presented to interpret the singular behavior of the density of states at certain negative energies. Our detailed analysis of the spin structure of Rashba billiards reveals a finite out-of-plane spin projection for electron eigenstates.Comment: 12 pages, 6 figures, minor changes in the text, submitted to PR

Unified Description of the Aharonov-Bohm Effect in Isotropic Multiband Electronic Systems

We present a unified treatment of the Aharonov--Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely that this cross section is {\it the same for all isotropic systems} and agrees with that obtained first by Aharonov and Bohm for spinless free particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.Comment: 4 pages, 2 figures in the main text and 22 pages in Supplemental Materia