Non-Hermitian bulk-boundary correspondence via scattering theory

TL;DR

This paper reestablishes the bulk-boundary correspondence in one-dimensional non-Hermitian systems using scattering theory, revealing new topological phases and phase transitions without traditional energy gap closing.

Contribution

It introduces a scattering theory approach to non-Hermitian topological systems, enabling topological invariant calculation without generalized Brillouin zone analysis.

Findings

Topological invariant obtained via generalized eigenproblem

Discovery of a critical topological phase without energy gap closing

Unveiling of a new phase with topological boundary states

Abstract

The conventional bulk-boundary correspondence breaks down in non-Hermitian systems. In this paper, we reestablish the bulk-boundary correspondence in one-dimensional non-Hermitian systems by applying the scattering theory, which is a systematical way in various symmetry classes. Based on the scattering theory, it is discovered that the topological invariant can be obtained by solving a generalized eigenproblem without calculating the generalized Brillouin zone. As a direct consequence, we unveil a new type of topological phase transition without typical bulk enengy gap closing and an unstable phase with topological boundary states, dubbed the critical topological phase.