Three-dimensional quantum Hall effect in Weyl semimetals

Abstract

We analytically study the three-dimensional (3D) quantum Hall effect (QHE) in a thin film of a Weyl semimetal from the perspective of bulk states. We derive the Chern numbers for $B\ensuremath{\ne}0$ from the Chern numbers for $B=0$ through a topological analysis and obtain a phase diagram of Chern numbers in Weyl semimetals. We demonstrate how the relative alignment of the Weyl nodes and the thickness of the film influence the quantum Hall plateaus and predict a peculiar phase diagram for the QHE in a thin film of a Weyl semimetal. Our work reveals the nature of the 3D QHE in Weyl semimetals from the bulk states.