Theory of the fractional quantum Hall effect in Weyl semimetals

TL;DR

This paper develops a three-dimensional hydrodynamic field theory for the fractional quantum Hall effect in Weyl semimetals, extending the well-known 2D Chern-Simons theory to 3D with a BF theory framework.

Contribution

It introduces a BF theory-based hydrodynamic model for 3D fractional quantum Hall states in magnetic Weyl semimetals, generalizing 2D theories.

Findings

Formulation of a 3D BF theory for fractional quantum Hall effect

Connection of the theory to quasiparticle and loop excitations

Extension of 2D Chern-Simons theory to 3D systems

Abstract

We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.