Bulk-boundary correspondence of non-Hermitian systems

An intriguing issue of non-Hermitian systems is the fate of bulk-boundary correspondence. We show that a previously overlooked ``non-Hermitian skin effect'' necessitates a non-Bloch bulk-boundary correspondence, which is based on a complex-valued Brillouin zone. This dramatic generalization of bulk-boundary correspondence is illustrated in the non-Hermitian Su-Schrieffer-Heeger models and Chern insulator models. We analytically obtain their topological phase diagrams, which are remarkably different from those of the Bloch Hamiltonians. As a natural formulation of the non-Bloch bulk-boundary correspondence, we introduce the non-Bloch topological invariants in the complex Brillouin zone (instead of the standard Brillouin zone with real-valued momentum), which faithfully predict the number of topological edge modes. Specifically, the chiral edge modes of two-dimensional non-Hermitian Chern bands are determined by the non-Bloch Chern numbers.
References:
[1] Shunyu Yao, Zhong Wang, Phys. Rev. Lett. 121, 086803 (2018)
[2] Shunyu Yao, Fei Song, Zhong Wang, Phys. Rev. Lett. 121, 136802 (2018)