Second-Order Topological Phases in Non-Hermitian Systems

Tao Liu (RIKEN)

Recently, there has been a great deal of interest in studying topological phases of open systems governed by non-Hermitian operators, altering the nature of the usual bulk-boundary correspondence in topological systems. Meanwhile, in the context of Hermitian topological systems, the concept of topological insulators has been generalized to higher-order topological insulators. In contrast to conventional first-order topological phases, a d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. In this poster, we will present our investigation of non-Hermitian seconder-order topological phases. It shows that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wave vectors is used to characterize the second-order topological phases in 2D (3D).