2020/07/31 by Yang Cao, Yang Li, Li Yang +1
Mathematics · Physics and Astronomy · #Bloch wave #Boundary (topology) #Boundary value problem #Brillouin zone #Combinatorics #Eigenvalues and eigenvectors #Floquet theory #Hamiltonian (control theory) #Hermitian matrix #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Periodic boundary conditions #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Topological Materials and Phenomena #Topology (electrical circuits) #Winding number #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.103.075126
published as Phys. Rev. B 103, 075126 (2021) · 8 pages, 4 figures
arxiv created 2020/08/01 · openalex publication_date 2021/02/15 · arxiv updated 2021/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the conventional bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits the non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether they are the bulk states or the zero and the \ensuremathπ 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,\ensuremathπ) characterize the edge states with quasienergies \ensuremathε=0,\ensuremathπ. In our non-Hermitian system, a novel phenomenon can emerge: the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show the relation between the non-Bloch winding numbers (W_0,\ensuremathπ) and the non-Bloch band invariant (W): W=W0\ensuremath-W_\ensuremathπ.