Wrapping Current versus Bulk Integer Quantum Hall Effect in Three Dimensions

TL;DR

This paper investigates the surface electron currents in the three-dimensional integer quantum Hall effect, revealing their relation to bulk properties and proposing an experiment to detect these currents.

Contribution

It predicts how surface currents in 3D quantum Hall systems wrap the sample and links them to 3D Chern numbers, extending the understanding of surface-bulk correspondence.

Findings

Surface currents wrap the facets of 3D samples.

Surface current intensity and direction are dictated by 3D Chern numbers.

An experimental setup is proposed to detect the 3D quantum Hall effect.

Abstract

Surface electron currents are studied for the integer quantum Hall effect in three dimensions(3D) proposed previously by Kohmoto et al. and by Koshino et al. We predict the current wraps the facets of the sample with its intensity and direction dictated by 3D Chern numbers which are just the quantized Hall conductivities in 3D ($\sigma_{xy}, \sigma_{zx}$), so a natural connection exists between the surface and bulk currents just as in 2D. An experiment to detect the 3D integer quantum Hall effect through the wrapping current is proposed.