Charge and current oscillations in Fractional quantum Hall systems with edges

TL;DR

This paper analyzes charge and current distributions in fractional quantum Hall systems with edges, revealing monotonic charge density in Hall bars and oscillatory modes in circular geometries, highlighting geometry-dependent behaviors.

Contribution

It introduces solutions for charge and current oscillations in fractional quantum Hall systems with different geometries using Chern-Simons theory, emphasizing the impact of system shape.

Findings

Charge density is monotonic in infinitely long Hall bar geometry.

Oscillatory charge density modes are present in disk and annulus geometries.

Charge and current can exist far from edges in compact geometries.

Abstract

Stationary solutions of the Chern-Simons effective field theory for the fractional quantum Hall systems with edges are presented for Hall bar, disk and annulus. In the infinitely long Hall bar geometry (non compact case), the charge density is shown to be monotonic inside the sample. In sharp contrast, spatial oscillatory modes of charge density are found for the two circular geometries, which indicate that in systems with compact geometry, charge and current exist also far from the edges.