Analytic density of states of two-dimensional Chern insulator

TL;DR

This paper derives exact analytical expressions for the density of states of the two-dimensional Qi-Wu-Zhang Hamiltonian, a model for Chern topological insulators, expressed via elliptical integrals, aiding in understanding their physical properties.

Contribution

It provides the first explicit analytical formulas for the density of states of the QWZ Hamiltonian, including spectral moments, useful for studying non-interacting and interacting Chern insulators.

Findings

Analytic density of states expressed in elliptical integrals.

Special cases of dispersion relations and densities of states analyzed.

Spectral moments calculated for the QWZ model.

Abstract

We present analytic expressions for the density of states and its consistent derivation for the two-dimensional Qi-Wu-Zhang (QWZ) Hamiltonian, a generic model for the Chern topological insulators of class A. This density of states is expressed in terms of elliptical integrals. We discuss and plot special cases of the dispersion relations and the corresponding densities of states. Spectral moments are also presented. The exact formulae ought to be useful in determining physical properties of the non-interacting Chern insulators and within the dynamical mean-field theory for interacting fermions with the QWZ Hamiltonian in the non-interacting limit.