Non-Hermitian Topology in Hermitian Topological Matter

TL;DR

This paper uncovers a hidden link between Hermitian and non-Hermitian topologies, demonstrating how boundary states in Hermitian topological insulators exhibit non-Hermitian characteristics through self-energy analysis.

Contribution

It introduces a novel framework connecting Hermitian topological insulators with non-Hermitian topology via boundary self-energy, classifies this correspondence across all symmetry classes.

Findings

Boundary states in Hermitian insulators show non-Hermitian topology.

Self-energy captures the connection between bulk Hermitian and boundary non-Hermitian topology.

Identification of non-Hermitian skin effect and hinge states in topological materials.

Abstract

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our work uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.