Bulk-boundary correspondence in point-gap topological phases

TL;DR

This paper establishes the bulk-boundary correspondence in non-Hermitian systems with point-gap topology, revealing how open boundary conditions affect topological classifications and lead to robust surface states.

Contribution

It provides the first comprehensive classification of open boundary point-gap topology in non-Hermitian systems with symmetry using real space invariants and K-theory.

Findings

Bulk point-gap topology can differ between open and periodic boundaries.

Nontrivial open boundary topology results in robust surface states.

Complete classification of open boundary point-gap topology with symmetry.

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.