Spin susceptibility of three-dimensional Dirac semimetals

TL;DR

This paper provides a theoretical analysis of the spin susceptibility in three-dimensional Dirac semimetals, deriving analytical formulas and exploring dependencies on cutoff energy and mass, with implications for topological insulators.

Contribution

It offers new analytical expressions for spin susceptibility in Dirac semimetals, including effects of mass and cutoff energy, and compares lattice model results with continuum theory.

Findings

Spin susceptibility is independent of Fermi energy.

Susceptibility depends on cutoff energy and band parameters.

Results apply to both massless and massive Dirac fermions.

Abstract

We theoretically study the spin susceptibility of Dirac semimetals using the linear response theory. The spin susceptibility is decomposed into an intraband contribution and an interband contribution. We obtain analytical expressions for the intraband and interband contributions of massless Dirac fermions. The spin susceptibility is independent of the Fermi energy while it depends on the cutoff energy, which is introduced to regularize the integration. We find that the cutoff energy is appropriately determined by comparing the results for the Wilson-Dirac lattice model, which approximates the massless Dirac Hamiltonian around the Dirac point. We also calculate the spin susceptibility of massive Dirac fermions for the model of topological insulators. We discuss the effect of the band inversion and the strength of spin-orbit coupling.