Finite-temperature relativistic Landau problem and the relativistic quantum Hall effect

TL;DR

This paper investigates the relativistic Landau problem at finite temperature, analyzing free energy, particle density, and Hall conductivity, revealing insights into the quantum Hall effect in a relativistic quantum field context.

Contribution

It introduces a comprehensive analysis of the relativistic Landau problem at finite temperature, including Hall conductivity derivation via Lorentz boost techniques.

Findings

Finite-temperature free energy and particle density calculated.

Hall conductivity derived in crossed electric and magnetic fields.

Connection established between relativistic Landau levels and quantum Hall effect.

Abstract

This paper presents a study of the free energy and particle density of the relativistic Landau problem, and their relevance to the quantum Hall effect. We study first the zero temperature Casimir energy and fermion number for Dirac fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform magnetic field perpendicular to the spatial manifold. Then, we go to the finite-temperature problem, with a chemical potential, introduced as a uniform zero component of the gauge potential. By performing a Lorentz boost, we obtain Hall's conductivity in the case of crossed electric and magnetic fields.