Magnetic scattering of Dirac fermions in topological insulators and graphene

We study quantum transport and scattering of massless Dirac fermions by spatially localized static magnetic fields. The employed model describes in a unified manner the effects of orbital magnetic fields, Zeeman and exchange fields in topological insulators, and the pseudo-magnetic fields caused by strain or defects in monolayer graphene. The general scattering theory is formulated, and for radially symmetric fields, the scattering amplitude and the total and transport cross sections are expressed in terms of phase shifts. As applications, we study ring-shaped magnetic fields (including the Aharanov-Bohm geometry) and scattering by magnetic dipoles.Comment: 11 pages, 4 figure

Statistical Ensembles and Spectral Correlations in Mesoscopic Systems

Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles due to both quenched disorder and thermodynamical effects. We show how these differences are related to spectral correlations of the system at hand, and evaluate the conditions (temperature, system's size) when the thermodynamic limit is achieved. We demonstrate our approach by evaluating the heat capacity, persistent currents and the occupation probability of single electron states, employing a systematic diagrammatic approach.Comment: 18 pages, Latex, 7 figures available by request, submitted to special issue of "Chaos, Solitons & Fractals" on "Chaos and Quantum Transport in Mesoscopic Cosmos

Keldysh Ginzburg-Landau action of fluctuating superconductors

We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor'kov-Eliashberg coupling between $\Delta$ and the scalar potential, as well as a peculiar nonlocal nonlinear term. The action is gauge invariant and satisfies the fluctuation dissipation theorem. It may be employed e.g. for calculation of higher moments of the current fluctuations.Comment: 16 pages, 2 figure

Interaction corrections to tunneling conductance in ballistic superconductors

It is known that in the two-dimensional disordered superconductors electron-electron interactions in the Cooper channel lead to the negative logarithmic in temperature correction to the tunneling conductance above the critical temperature. Physically this result appears due to the density of states suppression by superconductive fluctuations near the Fermi level. It is interesting that the other correction, which accounts for the Maki-Thompson-type interaction of fluctuations, is positive and exhibits strong power law, which dominates the logarithmic term in the immediate vicinity of the critical temperature. An interplay between these two contributions determines the zero-bias anomaly in fluctuating superconductors. This paper is devoted to the fate of such interaction corrections in the ballistic superconductors. It turns out that ballistic dynamic fluctuations perturb single-particle density of states near the Fermi level at the energy scale which is different from that in the diffusive case. As the consequence, fluctuation region becomes much broader. In this regime we confirm that correction to the tunneling conductance remains negative and logarithmic not too close to the critical temperature while in the immediate vicinity of the transition we find novel power law for the Maki-Thompson contribution. It is suggested that peculiar non-monotonous temperature dependence of the tunneling conductance may be probed via magneto-tunnel experiments.Comment: 4 pages, 2 figure

Zero--Bias Anomaly in Finite Size Systems

The small energy anomaly in the single particle density of states of disordered interacting systems is studied for the zero dimensional case. This anomaly interpolates between the non--perturbative Coulomb blockade and the perturbative limit, the latter being an extension of the Altshuler--Aronov zero bias anomaly at d=0. Coupling of the zero dimensional system to a dissipative environment leads to an effective screening of the interaction and a modification of the density of states.Comment: 25 pages and 6 figure

Point-charge electrostatics in disordered alloys

A simple analytic model of point-ion electrostatics has been previously proposed in which the magnitude of the net charge q_i on each atom in an ordered or random alloy depends linearly on the number N_i^(1) of unlike neighbors in its first coordination shell. Point charges extracted from recent large supercell (256-432 atom) local density approximation (LDA) calculations of Cu-Zn random alloys now enable an assessment of the physical validity and accuracy of the simple model. We find that this model accurately describes (i) the trends in q_i vs. N_i^(1), particularly for fcc alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges and Coulomb shifts (i.e., the average over all sites occupied by either $A$ or $B$ atoms) in the random alloy, and (iv) the linear relation between the site charge q_i and the constant- charge-averaged Coulomb shift (i.e., the average over all sites with the same charge) for fcc alloys. However, for bcc alloys the fluctuations predicted by the model in the q_i vs. V_i relation exceed those found in the LDA supercell calculations. We find that (a) the fluctuations present in the model have a vanishing contribution to the electrostatic energy. (b) Generalizing the model to include a dependence of the charge on the atoms in the first three (two) shells in bcc (fcc) - rather than the first shell only - removes the fluctuations, in complete agreement with the LDA data. We also demonstrate an efficient way to extract charge transfer parameters of the generalized model from LDA calculations on small unit cells.Comment: 15 pages, ReVTeX galley format, 7 eps figures embedded using psfig, to be published in Phys. Rev.

Magnetic Symmetries and Vortices In Chern-Simons Theories

We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $\kappa$ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small $\kappa$. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.Comment: 21 pages, laTe

Keldysh technique and non-linear sigma-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear sigma-model for disordered metals and superconductors. We discuss such topics as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equation, etc. The sections devoted to disordered superconductors include Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a substantial extension of arXiv:cond-mat/0412296.)Comment: Review: 103 pages, 19 figure

Numerical simulations based on probe measurements in EUV-induced hydrogen plasma

We use the two-dimensional particle-in-cell model with Monte Carlo collisions to study the plasma induced in hydrogen by short pulses of extreme ultraviolet (EUV) radiation at wavelengths in the range 10-20 nm with a pulse duration of about 40 ns (FWHM). This plasma is formed via both photoionization by the high-energy EUV photons and by the secondary photoelectrons emitted from the hydrogen molecules and the irradiated surface. The latter process can be enhanced by the external electric field that accelerates the electrons. In order to establish a base for our model so as to obtain accurate results, we record a temporally-resolved series of current-voltage characteristics for a small probing electrode inserted into EUV-induced hydrogen plasma. We then resort to simulating this plasma in the same geometry with the probe in our model which we validate by matching its results to the experimentally measured dynamics of the probe current-voltage curves. Having validated the model this way, we use this model as an independent instrument capable of obtaining the spatiotemporal picture of EUV-induced plasma evolution. We use this instrument to study the plasma formation during the EUV pulse and point out the processes that take part in forming this plasma, such as impact ionization and direct ionization by EUV photons