Edge states and topological invariants of non-Hermitian systems

2018/03/31 by Shunyu Yao, Zhong Wang · 15 citations
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.other #cond-mat.quant-gas #cond-mat.str-el #physics.optics

paper · pdf · doi:10.1103/physrevlett.121.086803

published as Phys. Rev. Lett. 121, 086803 (2018) · 9 pages, 7 figures. PRL Editors' Suggestion

arxiv created 2018/09/06 · arxiv updated 2018/09/07

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 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.

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