Edge spin transport in disordered two-dimensional topological insulators

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, for the first time, the spin current operator for the helical edge modes of a 2D TI. 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 then utilize a tight-binding model of topological monolayer WTe₂ 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 scalar and 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 symmetry-breaking perturbations as long as inter-edge scattering is weak.