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

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 Středa formula is employed to describe how the anomalous magnetization is related to the anomalous Hall effect. (paper)