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

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, to clarify the universality of real-space topological invariant in non-Hermitian systems, we elucidate that ${Q}_{xy}$ is also applicable for samples with the non-Hermitian skin effect. Our work enlightens the study of the combination of disorder and non-Hermitian HOTI.