Bulk charge distributions on integer and fractional quantum Hall plateaus

TL;DR

This paper analyzes charge distributions in a 2D electron gas on quantum Hall plateaus, revealing that fractional cases can exhibit alternating induced charge signs, using a response function approach and Wiener-Hopf method.

Contribution

It introduces a novel analysis of bulk charge distributions on fractional quantum Hall plateaus, extending previous integer case studies with new findings on charge sign alternation.

Findings

Induced charge can alternate in sign in fractional quantum Hall states.

The analysis employs a response function relation and Wiener-Hopf method.

Provides insights into charge behavior across quantum Hall regimes.

Abstract

We discuss the charge distributions across the bulk of a two-dimensional electron gas system which is on an integer or fractional quantum Hall plateau. Our analysis is based on a relation, derived from the long wavelength limit of the bulk density-density response function, between the induced charge and leading derivatives of a slowly varying Hall potential. We use the Wiener-Hopf method to solve the coupled response and Poisson equations. Unlike the integer case, treated in previous work, the induced charge in the fractional case can alternate in sign.