Non-Hermitian topology of quantum spin-Hall systems to detect edge-state polarization

TL;DR

This paper investigates how non-Hermitian topology emerges in quantum spin-Hall systems through transport imbalances, proposing the non-Hermitian skin effect as a sensitive method to detect edge-state spin polarization.

Contribution

It identifies mechanisms for non-Hermitian topology in quantum spin-Hall systems and introduces the non-Hermitian skin effect as a diagnostic tool for edge-state polarization.

Findings

Non-Hermitian topology arises from transport imbalance, not just time-reversal symmetry breaking.

Spin polarization-dependent responses can probe edge-state polarization.

Non-Hermitian skin effect is more sensitive than conductance to detect edge-state spin polarization.

Abstract

We study the non-Hermitian topology of multi-terminal transport in a quantum spin-Hall device described by the Bernevig-Hughes-Zhang model. We show that breaking time-reversal symmetry alone does not imply non-reciprocal transport or a non-Hermitian conductance matrix. Instead, non-Hermitian topology arises only when transport becomes directionally imbalanced. We identify two distinct mechanisms that generate such a response: spin-selective coupling at the contacts and an out-of-plane Zeeman field that unbalances the counter-propagating helical edge modes. We show, for unpolarized leads, that the spin polarization-dependent response to Zeeman fields, provides a transport-based probe of the intrinsic spin polarization of the helical edge states. Moreover, we demonstrate that non-Hermitian skin effect is more sensitive than conductance elements to detect the spin polarization of the edge states. Our results clarify the conditions required for non-Hermitian topology in quantum spin-Hall transport and establish non-Hermitian skin effect as a diagnostic tool for spin-selective coupling and edge-state polarization.