Bulk-boundary correspondence in point-gap topological phases

• URL: http://arxiv.org/abs/2205.15635v4
• Date: Fri, 29 Mar 2024 10:24:25 GMT
• Title: Bulk-boundary correspondence in point-gap topological phases
• Authors: Daichi Nakamura, Takumi Bessho, Masatoshi Sato,
• Abstract summary: A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, the other is intrinsic to non-Hermitian systems. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the $K$-theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.

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