Topological invariants of complex energy plane in non-Hermitian systems

TL;DR

This paper introduces a new topological invariant framework for non-Hermitian systems, linking pseudo-boundary states in the complex energy plane to topological phases, and demonstrates its application to non-Hermitian Chern insulators.

Contribution

It proposes a generalized local-global correspondence between pseudo-boundary states and topological invariants, revealing novel invariants and enriching the understanding of non-Hermitian topological phases.

Findings

Identification of topological invariants from pseudo-boundary states

Discovery of novel topological invariants in Chern insulators

Establishment of a generalized vorticity and flipping index

Abstract

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local-global correspondence and discuss the relationships between the local-global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.