Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System

Yang Cao, Yang Li, Xiaosen Yang

Published 2020-07-27Version 1

Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits non-Hermitian skin effects: all the eigenstates are localized at the boundary of the systems, whether the bulk states or the zero and the $\pi$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers ($W_{0,\pi}$) characterize the edge states with quasienergies $\epsilon=0, \pi$. In our non-Hermitian system, a novel phenomenon can emerge that the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch Chern number. We also show that the relation between the non-Bloch winding numbers and the Chern number of the Floquet bands: $C= W_{0}-W_{\pi}$.