Topological marker in three dimensions based on kernel polynomial method

TL;DR

This paper introduces an efficient kernel polynomial method to calculate topological markers in three-dimensional disordered systems, enabling better analysis of topological phase stability and transitions in realistic materials.

Contribution

The paper presents a novel, computationally efficient approach for evaluating topological markers in higher-dimensional disordered systems using the kernel polynomial method.

Findings

Reveals criteria for topological order invariance under disorder

Demonstrates the possibility of disorder-induced topological phase crossover

Captures quantum criticality near topological phase transitions

Abstract

The atomic-scale influence of disorder on the topological order can be quantified by a universal topological marker, although the practical calculation of the marker becomes numerically very costly in higher dimensions. We propose that for any symmetry class in higher dimensions, the topological marker can be calculated in a very efficient way by adopting the kernel polynomial method. Using class AII in three dimensions as an example, which is relevant to realistic topological insulators like Bi2Se3 and Bi2Te3, this method reveals the criteria for the invariance of topological order in the presence of disorder, as well as the possibility of a smooth cross over between two topological phases caused by disorder. In addition, the significantly enlarged system size in the numerical calculation implies that this method is capable of capturing the quantum criticality much closer to topological phase transitions, as demonstrated by a nonlocal topological marker.