Spin-charge separation and quantum spin Hall effect of $\beta$-bismuthene

TL;DR

This paper demonstrates spin-charge separation and quantized spin pumping in $eta$-bismuthene, establishing a new standard for predicting 2D quantum spin-Hall materials through topological invariants and real-space responses.

Contribution

It provides a proof of principle for spin-charge separation in realistic materials using ab initio band structures and topological analysis, advancing the understanding of quantum spin-Hall effects.

Findings

Spin-charge separation demonstrated in $eta$-bismuthene.

Quantized spin pumping observed in multiple insulating states.

Topologically non-trivial bands with even integer winding numbers identified.

Abstract

Field theory arguments suggest the possibility of $\mathbb{Z}$-classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the \emph{proof of principle} demonstration of spin-charge separation is yet to be accomplished for realistic, \emph{ab initio} band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on $\beta$-bismuthene to demonstrate spin-charge separation, and quantized pumping of spin for three insulating states that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of topologically non-trivial bands, supporting even integer winding numbers, which cannot be inferred from symmetry-based indicators. Our work sets a new standard for prediction of two-dimensional, quantum spin-Hall materials, based on precise bulk invariant and universal topological response.