Non-Hermitian Origin of Detachable Boundary States in Topological Insulators

TL;DR

This paper reveals that the phenomenon of detachable boundary states in certain topological insulators is fundamentally linked to non-Hermitian topology, providing a new classification framework for these states.

Contribution

It establishes a novel connection between detachable boundary states and non-Hermitian topology, extending the topological classification of Wannier localizability.

Findings

Intrinsic non-Hermitian topology causes spectral flow.

Extrinsic non-Hermitian topology explains boundary state detachment.

Complete tenfold classification of Wannier localizability and boundary states.

Abstract

While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non-Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. Based on this connection and $K$-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states.