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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.
A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable inte
The realization of the quantum anomalous Hall (QAH) effect without magnetic doping attracts intensive interest since magnetically doped topological insulators usually possess inhomogeneity of ferromagnetic order. Here, we propose a different strategy
It has been proposed that disorder may lead to a new type of topological insulator, called topological Anderson insulator (TAI). Here we examine the physical origin of this phenomenon. We calculate the topological invariants and density of states of
In this work, we study the disorder effects on the bulk-boundary correspondence of two-dimensional higher-order topological insulators (HOTIs). We concentrate on two cases: (i) bulk-corner correspondence, (ii) edge-corner correspondence. For the bulk
The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic picture promotes discover