Topological Anderson insulator in two-dimensional non-Hermitian systems**Project supported by the National Basic Research Program of China (Grant No. 2019YFA0308403), the National Natural Science Foundation of China (Grant No. 11822407), Undergraduate Training Program for Innovation and Entrepreneurship, Soochow University (Grant No. 201810285022Z), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

Abstract

We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method (NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems (a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly, we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength: (1) the normal insulator phase to the gapless phase, (2) the normal insulator phase to the topological Anderson insulator phase, and (3) the gapless phase to the topological Anderson insulator phase.