Thermodynamics of the system of massive Dirac fermions in a uniform magnetic field

TL;DR

This paper develops a thermodynamic framework for massive Dirac fermions in a magnetic field, deriving key quantities and effects, including the chiral magnetic and separation effects, with a focus on mass and magnetic susceptibility.

Contribution

It introduces a comprehensive thermodynamic analysis of massive Dirac fermions in magnetic fields, including expansions and corrections for mass effects and chiral phenomena.

Findings

Derived the grand partition function from Landau levels.

Expanded thermodynamic quantities using the Abel-Plana formula.

Recovered known chiral magnetic and separation effects in the massless limit.

Abstract

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel-Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable $b=2eB/T^{2}$. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass correction to chiral separation effect is discussed. For massless chiral fermions, our results recover the chiral magnetic effect for right- and left-handed fermions, as well as chiral separation effect.