Analytic approach to quantum metric and optical conductivity in Dirac models with parabolic mass in arbitrary dimensions

TL;DR

This paper analytically derives the quantum metric and optical conductivity for Dirac models with parabolic mass dispersion across arbitrary dimensions, revealing dimension-dependent optical responses and differences between topological phases.

Contribution

It provides the first analytical expressions for quantum metric and optical conductivity in Dirac models with parabolic mass dispersion in any dimension.

Findings

Optical conductivity at band-edge depends on dimension.

Quantum metric observable via optical conductivity influenced by parabolic coefficient.

Distinct optical responses between topological and trivial phases with same gap.

Abstract

The imaginary part of the quantum geometric tensor is the Berry curvature, while the real part is the quantum metric. Dirac fermions derived from a tight-binding model naturally contains a mass term $m(k)$ with parabolic dispersion, $m(k)=$ $m+uk^{2}$. However, in the Chern insulator based on Dirac fermions, only the sign of the mass $m$ is relevant. Recently, it was reported that the quantum metric is observable by means of the optical conductivity, which is significantly affected by the parabolic coefficient $% u $. We analytically obtain the quantum metric and the optical conductivity in the Dirac Hamiltonian in arbitrary dimensions, where the Dirac mass has parabolic dispersion. The optical conductivity at the band-edge frequency significantly depends on the dimensions. We also make an analytical study on the quantum metric and the optical conductivity in the Su-Schrieffer-Heeger model, the Qi-Wu-Zhang model and the Haldane model. The optical conductivity is found to be quite different between the topological and trivial phases even when the gap is taken identical.