Second-Order Topological Phases in Non-Hermitian Systems

A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. Here, we show 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). A possible…

• JT
  John Templeton Foundation
• MO
  Ministry of Education, Culture, Sports, Science and Technology
• CP
  China Postdoctoral Science Foundation

  Award: 2018M640055
• JS
  Japan Society for the Promotion of Science

  Awards: JP15H05855, P18023, VS.059.18N, JP18H01145, 17-52-50023
• JS
  Japan Science and Technology Agency

  Award: JPMJCR1676
• AF
  Air Force Office of Scientific Research

  Award: FA9550-14-1-0040
• AR
  Army Research Office

  Award: W911NF-18-1-0358