Magnetic susceptibility in three-dimensional nodal semimetals

TL;DR

This paper investigates the magnetic susceptibility in three-dimensional nodal semimetals, revealing divergent behaviors at band touching points and linking spin-orbit effects to topological surface currents.

Contribution

It provides a detailed analysis of the different susceptibility components in nodal semimetals and connects the spin-orbit cross term to topological surface phenomena.

Findings

Orbital susceptibility diverges logarithmically at band touching energy.

Line node susceptibility shows a delta-function singularity.

Spin-orbit cross term is paramagnetic for electrons and diamagnetic for holes.

Abstract

We study the magnetic susceptibility in various three-dimensional gapless systems, including Dirac and Weyl semimetals and a line-node semimetal. The susceptibility is decomposed into the orbital term, the spin term and also the spin-orbit cross term which is caused by the spin-orbit interaction. We show that the orbital susceptibility logarithmically diverges at the band touching energy in the point-node case, while it exhibits a stronger delta-function singularity in the line node case. The spin-orbit cross term is shown to be paramagnetic in the electron side while diamagnetic in the hole side, in contrast with other two terms which are both even functions in Fermi energy. The spin-orbit cross term in the nodal semimetal is found to be directly related to the chiral surface current induced by the topological surface modes.