Real-space calculation of the conductivity tensor for disordered topological matter

TL;DR

This paper presents a computational method using Chebyshev polynomial expansion to efficiently calculate the conductivity tensor in large disordered topological systems at various temperatures and chemical potentials.

Contribution

The authors introduce a novel numerical approach based on Bastin's formulation and Chebyshev polynomials for calculating conductivity tensors in disordered topological materials.

Findings

Successfully computed conductivity tensors for disordered graphene and Haldane's model.

Analyzed the impact of disorder on quantum Hall effect and Chern insulators.

Demonstrated the method's efficiency and versatility across different topological phases.

Abstract

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.