Thermodynamic properties of the 2+1-dimensional Dirac fermions with broken time-reversal symmetry

TL;DR

This paper investigates the thermodynamic behavior of 2+1D massive Dirac fermions with broken time-reversal symmetry in a magnetic field, revealing an anomalous, field-independent magnetization linked to the anomalous Hall effect.

Contribution

It provides a detailed analysis of the thermodynamic potential and magnetization, highlighting the anomalous magnetic response due to broken time-reversal symmetry.

Findings

Magnetization is independent of magnetic field strength.

Linear in field term in thermodynamic potential due to broken symmetry.

Connection between anomalous magnetization and anomalous Hall effect.

Abstract

We study the thermodynamic properties of the two-component $2+1$-dimensional massive Dirac fermions in an external magnetic field. The broken time-reversal symmetry results in the presence of a linear in the magnetic field part of the thermodynamic potential, while in the famous problem of Landau diamagnetism the leading field dependent term is quadratic in the field. Accordingly, the leading term of the explicitly calculated magnetization is anomalous, viz. it is independent of the strength of the magnetic field. The St\v{r}eda formula is employed to describe how the anomalous magnetization is related to the anomalous Hall effect.