“Edge States and Topological Invariants of Non-Hermitian Systems” (2018), by Shunyu Yao et al. Physics and Astronomy research paper. Original abstract below, unchanged. A free PDF is available.

Edge States and Topological Invariants of Non-Hermitian Systems

Shunyu Yao, Zhong Wang · August 21, 2018 · Physics and Astronomy

Abstract

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Free PDF DOI: 10.1103/physrevlett.121.086803