Singular Effects of Spin-Flip Scattering on Gapped Dirac Fermions

We investigate the effects of spin-flip scattering on the Hall transport and spectral properties of gapped Dirac fermions. We find that in the weak scattering regime, the Berry curvature distribution is dramatically compressed in the electronic energy spectrum, becoming singular at band edges. As a result the Hall conductivity has a sudden jump (or drop) of $e^2/2h$ when the Fermi energy sweeps across the band edges, and otherwise is a constant quantized in units of $e^2/2h$. In parallel, spectral properties such as the density of states and spin polarization are also greatly enhanced at band edges. Possible experimental methods to detect these effects are discussed

Electric-Field Breakdown of Absolute Negative Conductivity and Supersonic Streams in Two-Dimensional Electron Systems with Zero Resistance/Conductance States

We calculate the current-voltage characteristic of a two-dimensional electron system (2DES) subjected to a magnetic field at strong electric fields. The interaction of electrons with piezoelectric acoustic phonons is considered as a major scattering mechanism governing the current-voltage characteristic. It is shown that at a sufficiently strong electric field corresponding to the Hall drift velocity exceeding the velocity of sound, the dissipative current exhibits an overshoot. The overshoot of the dissipative current can result in a breakdown of the absolute negative conductivity caused by microwave irradiation and, therefore, substantially effect the formation of the domain structures with the zero-resistance and zero-conductance states and supersonic electron streams.Comment: 5 pages, 4 figure

Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity

The density of states and the Hall conductivity of a two-dimensional electron gas in a uniform magnetic field and in the presence of a delta impurity are exactly calculated using elementary field theoretic techniques. Although these results are not new, our treatment is explicitly gauge-invariant, and can be easily adapted to other problems involving a delta potential.Comment: 12+1 pages, 1 ps figure, REVTEX. Corrigendum adde

Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach

The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semi-classical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explcit calculations for the case of the two-dimensional (2D) Dirac model Hamiltonian relevant to graphene.Comment: 17 pages, 13 figure

Transverse Magnetoresistance of GaAs/AlGaAs Heterojunctions in the Presence of Parallel Magnetic Fields

We have calculated the resistivity of a GaAs\slash AlGaAs heterojunction in the presence of both an in--plane magnetic field and a weak perpendicular component using a semiclassical Boltzmann transport theory. These calculations take into account fully the distortion of the Fermi contour which is induced by the parallel magnetic field. The scattering of electrons is assumed to be due to remote ionized impurities. A positive magnetoresistance is found as a function of the perpendicular component, in good qualitative agreement with experimental observations. The main source of this effect is the strong variation of the electronic scattering rate around the Fermi contour which is associated with the variation in the mean distance of the electronic states from the remote impurities. The magnitude of the positive magnetoresistance is strongly correlated with the residual acceptor impurity density in the GaAs layer. The carrier lifetime anisotropy also leads to an observable anisotropy in the resistivity with respect to the angle between the current and the direction of the in--plane magnetic field.Comment: uuencoded file containing a 26 page RevTex file and 14 postscript figures. Submitted to Phys. Rev.

Weak Localization and Integer Quantum Hall Effect in a Periodic Potential

We consider magnetotransport in a disordered two-dimensional electron gas in the presence of a periodic modulation in one direction. Existing quasiclassical and quantum approaches to this problem account for Weiss oscillations in the resistivity tensor at moderate magnetic fields, as well as a strong modulation-induced modification of the Shubnikov-de Haas oscillations at higher magnetic fields. They do not account, however, for the operation at even higher magnetic fields of the integer quantum Hall effect, for which quantum interference processes are responsible. We then introduce a field-theory approach, based on a nonlinear sigma model, which encompasses naturally both the quasiclassical and quantum-mechanical approaches, as well as providing a consistent means of extending them to include quantum interference corrections. A perturbative renormalization-group analysis of the field theory shows how weak localization corrections to the conductivity tensor may be described by a modification of the usual one-parameter scaling, such as to accommodate the anisotropy of the bare conductivity tensor. We also show how the two-parameter scaling, conjectured as a model for the quantum Hall effect in unmodulated systems, may be generalized similarly for the modulated system. Within this model we illustrate the operation of the quantum Hall effect in modulated systems for parameters that are realistic for current experiments.Comment: 15 pages, 4 figures, ReVTeX; revised version with condensed introduction; two figures taken out; reference adde

Universal Fluctuation of the Hall Conductance in the Random Magnetic Field

We show that the RMS fluctuation of the antisymmetric part of the Hall conductance of a planar mesoscopic metal in a random magnetic field with zero average is universal, of the order of $e^2/h$, independent of the amplitude of the random magnetic field and the diffusion coefficient even in the weak field limit. This quantity is exactly zero in the case of ordinary scalar disorder. We propose an experiment to measure this surprising effect, and also discuss its implications on the localization physics of this system. Our result applies to some other systems with broken time-reversal ({\bf T}) symmetry.Comment: 4 pages, Revtex 3.0; added the paragraph regarding applicability to other systems with broken T-invariance, misc. minor change

A Model for the Voltage Steps in the Breakdown of the Integer Quantum Hall Effect

In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.Comment: 4 pages including 3 figure

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed