Analytical theory and possible detection of the $ac$ quantum spin Hall effect

TL;DR

This paper presents an analytical framework for the ac quantum spin Hall effect, linking it to bulk topological invariants and proposing an experimental detection method using ferromagnetic electrodes.

Contribution

It introduces an analytical scattering matrix approach to describe the ac QSH effect and connects it to bulk topological properties, also proposing a practical detection scheme.

Findings

The ac QSH effect can be viewed as a bulk quantum pumping process.

Quantized ac spin Hall conductivity relates to reflection matrix winding numbers.

A feasible experimental setup using ferromagnetic electrodes is proposed.

Abstract

We develop an analytical theory of the low-frequency $ac$ quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the $ac$ QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized $ac$ spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological $ac$ spin current by electrical means.