Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions

TL;DR

This paper provides an analytical study of magnetizations in massive Dirac fermions, exploring effects of magnetic field, temperature, impurities, and band-gap, with implications for graphene and related materials.

Contribution

It introduces a generalized analytical framework for magnetization and susceptibility in Dirac fermions, including impurity effects and band-gap dependence, extending previous models.

Findings

Large band-gap yields robust magnetization against temperature and impurities.

Impurity effects cause susceptibility to follow a Faddeeva function-based scaling law.

Band-gap influences the period and amplitude of de Haas-van Alphen oscillations.

Abstract

We theoretically study magnetic field, temperature, and energy band-gap dependences of magnetizations in the Dirac fermions. We use the zeta function regularization to obtain analytical expressions of thermodynamic potential, from which the magnetization of graphene for strong field/low temperature and weak field/high temperature limits are calculated. Further, we generalize the result by considering the effects of impurity on orbital susceptibility of graphene. In particular, we show that in the presence of impurity, the susceptibility follows a scaling law which can be approximated by the Faddeeva function. In the case of the massive Dirac fermions, we show that a large band-gap gives a robust magnetization with respect to temperature and impurity. In the doped Dirac fermion, we discuss the dependence of the band-gap on the period and amplitude of the de Haas-van Alphen effect.