Quantum Hall effective action for anisotropic Dirac semi-metal

TL;DR

This paper develops a covariant effective action framework to analyze Hall transport in anisotropic Dirac semi-metals, revealing how geometric and electromagnetic factors influence Hall responses.

Contribution

It introduces a novel covariant formulation for anisotropic Dirac semi-metals and derives an effective action capturing Hall transport phenomena.

Findings

Effective action consistent with PT symmetry

Identification of geometric contributions to Hall transport

Analysis of scaling symmetry in semi-Dirac phases

Abstract

We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.