Edge states and topological invariants of non-Hermitian systems

TL;DR

This paper reveals how the non-Hermitian skin effect alters topological invariants and phase diagrams in non-Hermitian systems, leading to a generalized bulk-boundary correspondence based on non-Bloch winding numbers.

Contribution

It introduces a non-Bloch bulk-boundary correspondence framework that accounts for the non-Hermitian skin effect, redefining topological invariants in non-Hermitian topological phases.

Findings

Phase diagrams differ significantly from traditional Bloch theory.

Topological zero modes are determined by non-Bloch winding numbers.

The work resolves the breakdown of conventional bulk-boundary correspondence.

Abstract

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked `non-Hermitian skin effect' necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.