Transport in a Nearly Periodic Potential with a Magnetic Field

TL;DR

This paper investigates the electronic properties of a two-dimensional quasiparticle gas in a nearly periodic potential with a magnetic field, revealing how randomness affects the density of states and Hall conductivity.

Contribution

It introduces a model using Dirac fermions with random parameters to analyze the effects of disorder on transport in nearly periodic systems under magnetic fields.

Findings

Density of states exhibits a singular form with an exponent decreasing with disorder strength.

Hall conductivity shows a plateau that disappears with increased tunneling through potential saddle points.

The model captures the transition from ordered to disordered transport regimes.

Abstract

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential and a perpendicular magnetic field is studied. The potential is a superposition of a periodic potential, induced e.g. by a charge density wave or a vortex lattice of a type--II superconductor, and a weak random potential due to impurities. Approximating this model by Dirac fermions with random mass, random energy, and random vector potential, we evaluate the density of states and the Hall conductivity using a self-consistent approximation. We obtain a singular average density of states $\rho(E)\approx\rho_0 +|E|^\alpha$, where $\alpha$ decreases with the strength of randomness. The Hall conductivity has a plateau which is destroyed for strong tunneling through the saddle points of the nearly periodic potential.