Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems

TL;DR

This paper introduces a real space topological invariant for non-Hermitian higher-order topological insulators and demonstrates disorder-induced phase transitions to a topologically nontrivial phase.

Contribution

It defines a quantized quadrupole moment as a topological invariant in non-Hermitian systems and explores disorder effects leading to a higher-order topological Anderson insulator.

Findings

Quadrupole moment $Q_{xy}$ is a quantized real space topological invariant.

Disorder induces a phase transition from normal insulator to HOTAI.

Invariant $Q_{xy}$ applies even with the non-Hermitian skin effect.

Abstract

We study the characterization and realization of higher-order topological Anderson insulator (HOTAI) in non-Hermitian systems, where the non-Hermitian mechanism ensures extra symmetries as well as gain and loss disorder.We illuminate that the quadrupole moment $Q_{xy}$ can be used as the real space topological invariant of non-Hermitian higher-order topological insulator (HOTI). Based on the biorthogonal bases and non-Hermitian symmetries, we prove that $Q_{xy}$ can be quantized to $0$ or $0.5$. Considering the disorder effect, we find the disorder-induced phase transition from normal insulator to non-Hermitian HOTAI. Furthermore, we elucidate that the real space topological invariant $Q_{xy}$ is also applicable for systems with the non-Hermitian skin effect. Our work enlightens the study of the combination of disorder and non-Hermitian HOTI.