The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

TL;DR

This paper develops a numerical method to accurately compute the longitudinal conductance of 2D electron systems under magnetic fields with disorder and periodic modulations, aligning well with recent experimental observations.

Contribution

It introduces an exact, scalable computational approach for analyzing the interplay of disorder and periodic modulations in quantum Hall systems, applicable to various geometries.

Findings

Numerical results agree qualitatively with recent experiments.

Method effectively accounts for disorder and periodic effects.

Approach can be extended to multi-terminal and multi-channel systems.

Abstract

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.