Bulk-Boundary Correspondence in Point-Gap Topological Phases

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.