Spin Hall and inverse spin galvanic effects in graphene with strong interfacial spin-orbit coupling: A quasi-classical Green's function approach

Van der Waals heterostructures assembled from atomically thin crystals are ideal model systems to study spin-orbital coupled transport because they exhibit a strong interplay between spin, lattice, and valley degrees of freedom that can be manipulated by strain, electric bias, and proximity effects. The recently predicted spinhelical regime in graphene on transition metal dichalcogenides, in which spin and pseudospin degrees of freedom are locked together [Offidani et al., Phys. Rev. Lett. 119, 196801 (2017)] suggests their potential application in spintronics. Here, by deriving an Eilenberger equation for the quasiclassical Green's function of two-dimensional Dirac fermions in the presence of spin-orbit coupling (SOC) and scalar disorder, we obtain analytical expressions for the dc spin galvanic susceptibility and spin Hall conductivity in the spin-helical regime. Our results disclose a sign change in the spin Hall angle (SHA) when the Fermi energy relative to the Dirac point matches the Bychkov-Rashba energy scale, irrespective of the magnitude of the spin-valley interaction imprinted on the graphene layer. The behavior of the SHA is connected to a reversal of the total internal angular momentum of Bloch electrons that reflects the spin-pseudospin entanglement induced by SOC. We also show that the chargeto-spin conversion efficiency reaches a maximum when the Fermi level lies at the edge of the spin-minority band in agreement with previous findings. Both features are fingerprints of spin-helical Dirac fermions and suggest a direct way to estimate the strength of proximity-induced SOC from transport data. The relevance of these findings for interpreting recent spin-charge conversion measurements in nonlocal spin-valve geometry is also discussed.