Optical Hall conductivity of systems with gapped spectral nodes

TL;DR

This paper calculates the optical Hall conductivity in systems with gapped spectral nodes, revealing its dependence on dispersion exponent, frequency, and robustness against disorder and thermal fluctuations.

Contribution

It provides a theoretical analysis of optical Hall conductivity for systems with power-law spectral nodes, highlighting the effects of dispersion and disorder.

Findings

Optical Hall conductivity is proportional to the dispersion exponent n.

A logarithmic singularity appears near the gap energy in conductivity.

Disorder impacts transport more strongly for n=2 than for n=1.

Abstract

We calculate the optical Hall conductivity within the Kubo formalism for systems with gapped spectral nodes, where the latter have a power-law dispersion with exponent n. The optical conductivity is proportional to n and there is a characteristic logarithmic singularity as the frequency approaches the gap energy. The optical Hall conductivity is almost unaffected by thermal fluctuations and disorder for n=1, whereas disorder has a stronger effect on transport properties if n=2.