Edge spin transport in the disordered two-dimensional topological insulator WTe$_2$

TL;DR

This paper investigates how disorder and perturbations affect spin conductance in 2D topological insulators, revealing robustness of spin Hall conductance under certain conditions through theoretical and numerical analysis.

Contribution

It introduces a formalism for measuring spin conductance in 2D TIs and studies the effects of disorder and inter-edge scattering using a tight-binding model of WTe$_2$.

Findings

Spin Hall conductance remains robust with weak inter-edge scattering.

Spin decay length is affected by magnetic disorder.

Spin conductance is resilient as long as time-reversal symmetry is preserved.

Abstract

The spin conductance of two-dimensional topological insulators (2D TIs) is not expected to be quantized in the presence of perturbations that break the spin-rotational symmetry. However, the deviation from the pristine-limit quantization has yet to be studied in detail. In this paper, we define the spin current operator for the helical edge modes of a 2D TI and introduce a four-terminal setup to measure spin conductances. Using the developed formalism, we consider the effects of disorder terms that break spin-rotational symmetry or give rise to edge-to-edge coupling. We identify a key role played by spin torque in an out-of-equilibrium edge. We then utilize a tight-binding model of topological monolayer WTe$_2$ and scattering matrix formalism to numerically study spin transport in a four-terminal 2D TI device. In particular, we calculate the spin conductances and characteristic spin decay length in the presence of magnetic disorder. In addition, we study the effects of inter-edge scattering in a quantum point contact geometry. We find that the spin Hall conductance is surprisingly robust to spin symmetry-breaking perturbations, as long as time-reversal symmetry is preserved and inter-edge scattering is weak.