Spin Hall Effect: Symmetry Breaking, Twisting, and Giant Disorder Renormalization

Atomically-thin materials based on transition metal dichalcogenides and graphene offer a promising avenue for unlocking the mechanisms underlying the spin Hall effect (SHE) in heterointerfaces. Here, we develop a microscopic theory of the SHE for twisted van der Waals heterostructures that fully incorporates twisting and disorder effects, and illustrate the critical role of symmetry breaking in the generation of spin-Hall currents. We find that an accurate treatment of vertex corrections leads to a qualitatively and quantitatively different SHE than that obtained from popular approaches like the ``$i\,\eta$'' and ladder approximations. A pronounced oscillatory behavior of skew-scattering processes with twist angle, $\theta$, is predicted, reflecting a non-trivial interplay of Rashba and valley-Zeeman effects and yields a vanishing SHE for $\theta = 30^\circ$ and, for graphene-WSe$_2$, an optimal SHE for $\theta \approx 17^\circ$. Our findings reveal disorder and broken symmetries as important knobs to optimize interfacial SHEs.