Currents in the Compressible and Incompressible Regions of the 2DEG

TL;DR

This paper derives a comprehensive expression for current distribution in a 2D electron gas under magnetic fields, revealing an intricate pattern of edge and bulk currents influenced by local density and potential gradients.

Contribution

It introduces a unified, self-consistent formula for current distribution in 2DEG, accounting for both edge and bulk currents on scales larger than the magnetic length.

Findings

Edge current proportional to local density gradient

Bulk current proportional to potential gradient

Currents exhibit alternating directional pattern

Abstract

We derive a general expression for the low-temperature current distribution in a two-dimensional electron gas, subjected to a perpendicular magnetic field and in a confining potential that varies slowly on the scale of the magnetic length l. The analysis is based on a self-consistent one-electron description, such as the Hartree or standard Kohn-Sham equations. Our expression, which correctly describes the current distribution on scales larger than l, has two components: One is an ``edge current'' which is proportional to the local density gradient and the other is a ``bulk current'' which is proportional to the gradient of the confining potential. The direction of these currents generally displays a striking alternating pattern.