Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure

TL;DR

This paper analyzes spin transport in time-reversal symmetric honeycomb insulators, showing that spin conductivity is generally not quantized and is not directly linked to topological indices, with detailed theoretical derivations and results.

Contribution

It provides a rigorous derivation of spin conductivity in these insulators and demonstrates the lack of universal quantization and its independence from topological indices.

Findings

Spin conductivity is well-defined and independent of spin current choice.

Deviations from quantization are quadratic in spin-non-conserving terms.

Spin conductivity is not universally quantized and not directly related to the Fu--Kane--Mele index.

Abstract

We investigate spin transport in a class of time-reversal symmetric insulators on the honeycomb structure, the Kane--Mele model being an emblematic example in this class. We derive the spin conductivity by the linear response \`a la Kubo and show that it is well-defined and independent of the choice of the spin current. For models that do not conserve the spin, we demonstrate that the deviation of the spin conductivity from the quantised value is, at worst, quadratic in the spin-non-conserving terms, thus improving previous results. Additionally, we show that the leading-order corrections are actually quadratic for some models in the class, demonstrating that the spin conductivity is not universally quantised. Consequently, our results show that, in general, there is no direct connection between the spin conductivity and the Fu--Kane--Mele index.