Edge spin transport in the disordered two-dimensional topological insulator WTe2

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 ${\mathrm{WTe}}_{2}$ 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 interedge 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 interedge scattering is weak.