Diffusive transport in the lowest Landau level of disordered 2d semimetals: the mean-square-displacement approach

TL;DR

This paper investigates electronic transport in the lowest Landau level of disordered 2D semimetals under magnetic fields, using a mean squared displacement approach to understand diffusion and conductivity influenced by Berry curvature effects.

Contribution

It introduces an analytical self-consistent method to analyze diffusion and conductivity in disordered 2D semimetals with Landau levels, highlighting the role of zero energy modes.

Findings

Zero mode conductivity is similar to that of disordered Dirac electrons without magnetic fields.

Intrinsic Berry curvature significantly affects the density of states and static conductivity.

The approach applies broadly to disordered 2D electron gases in strong magnetic fields.

Abstract

We study the electronic transport in the lowest Landau level of disordered two-dimensional semimetals placed in a homogeneous perpendicular magnetic field. The material system is modeled by the Bernevig-Hughes-Zhang Hamiltonian, which has zero energy Landau modes due to the material's intrinsic Berry curvature. These turn out to be crucially important for the density of states and the static conductivity of the disordered system. We develop an analytical approach to the diffusion and conductivity based on a self-consistent equation of motion for the mean squared displacement. The obtained value of the zero mode conductivity is close to the conductivity of disordered Dirac electrons without magnetic fields, which have zero energy points in the spectrum as well. Our analysis is applicable in a broader context of disordered two-dimensional electron gases in strong magnetic fields.