Bulk-Boundary Correspondence in a Non-Hermitian Chern Insulator

TL;DR

This paper extends the non-Hermitian bulk-boundary correspondence concept from one-dimensional topological insulators to two-dimensional Chern insulators, demonstrating that topological invariants predict boundary states even with gain/loss non-Hermiticity.

Contribution

It adapts a non-Hermitian bulk-boundary correspondence scenario to 2D Chern insulators, establishing a link between bulk topological numbers and boundary states in non-Hermitian systems.

Findings

Bulk Chern number correlates with boundary states in non-Hermitian insulators.

The approach enables phase diagram determination in boundary geometry.

Bulk-boundary correspondence holds for gain/loss non-Hermitian Chern insulators.

Abstract

A scenario of non-Hermitian bulk--boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk geometry under a modified periodic boundary condition and boundary geometry under an open boundary condition. The bulk geometry is used to define a topological number, whereas the boundary geometry is used to observe the presence or absence of a topological boundary state. It is demonstrated that the bulk--boundary correspondence holds in a two-dimensional Chern insulator with gain/loss-type non-Hermiticity; a nontrivial Chern number calculated in the bulk geometry is in one-to-one correspondence with the presence of a topological boundary state in the boundary geometry. This approach enables us to determine a phase diagram in the boundary geometry.