Quantum Valley Hall Effect in Massive Dirac Systems Coupled to a Scalar Field

TL;DR

This paper investigates how coupling a massive scalar field to (2+1)D Dirac systems affects the Quantum Valley Hall Effect, finding no change to the Quantum Hall Effect and a mass-dependent correction to the Valley Hall Effect.

Contribution

It introduces the analysis of scalar field interactions in Dirac systems, revealing non-universal corrections to the Quantum Valley Hall Effect.

Findings

No correction to the Quantum Hall Effect

Non-universal, mass ratio-dependent correction to the Quantum Valley Hall Effect

Scalar coupling influences the valley-dependent phenomena

Abstract

We use Pseudo Quantum Electrodynamics to study massive (2+1)D Dirac systems interacting electromagnetically via a U(1) gauge field in (3+1)D. It was recently found in Ref. [1], that an interaction-induced Quantum Hall Effect (QHE) and Quantum Valley Hall Effect (QVHE) occur in these systems, when considering a two-component fermion representation. Here, we study the corrections to these effects when coupling the fermions to a (2+1)D massive scalar field via a quartic interaction. We find no correction to the QHE and a non-universal correction to the QVHE, which depends on the ratio of the fermion and scalar-field masses.