Non-Bloch bands in two-dimensional non-Hermitian systems

TL;DR

This paper extends non-Bloch band theory to two-dimensional non-Hermitian systems, enabling the analysis of topological properties and edge states through a generalized Brillouin zone, thus broadening understanding beyond 1D models.

Contribution

The work develops a non-Bloch band theory for 2D non-Hermitian systems by reducing the problem to 1D models, establishing a generalized Brillouin zone and topological bulk-edge correspondence.

Findings

Generalized Brillouin zone constructed for 2D non-Hermitian systems

Topological bulk-edge correspondence demonstrated in non-Hermitian Chern insulator

Extension of non-Bloch band theory beyond 1D systems

Abstract

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether the non-Bloch band theory can be extended to higher-dimensional non-Hermitian systems is nontrivial. In this work, we construct the non-Bloch band theory in two classes of two-dimensional non-Hermitian systems, by reducing the problem to that for a 1D non-Hermitian model. In these classes of systems, we get the generalized Brillouin zone for a complex wavevector and investigate topological properties. In the model of the non-Hermitian Chern insulator, as an example, we show the bulk-edge correspondence between the Chern number defined from the generalized Brillouin zone and the appearance of the edge states.