Orbital magnetic susceptibility of type-I, II, and III massless Dirac fermions in two dimensions

TL;DR

This paper investigates the orbital magnetic susceptibility of different types of massless Dirac fermions in two dimensions, revealing distinct magnetic responses for types I, II, and III through continuum and lattice models.

Contribution

It clarifies the magnetic susceptibility behavior of tilted Dirac fermions across different types using both continuum and lattice models, highlighting new distinctions among them.

Findings

Type-I Dirac fermions have diverging diamagnetic susceptibility.

Type-II Dirac fermions show non-diverging paramagnetic susceptibility.

Type-III Dirac fermions exhibit small diamagnetism.

Abstract

We study the orbital magnetic susceptibility of tilted massless Dirac fermions in two dimensions. It is well-known that the type-I massless Dirac fermions exhibit divergingly-large diamagnetic susceptibility, whereas less is known about the types II and III cases. We first clarify that the orbital magnetic susceptibility is vanishing for the types II and III in the continuum model. We then compare the three types of Dirac fermions for the lattice models. We employ three tight-binding models with different numbers of Dirac points, all of which are two-band models defined on a square lattice. For all three models, we find that the type-I Dirac fermions show the divergingly-large orbital diamagnetic susceptibility, whereas the type-II Dirac fermions exhibit non-diverging paramagnetic susceptibility. The type-III Dirac fermions exhibit diamagnetism but its susceptibility is small compared with the type-I case.