  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 spin-helical regime in graphene on transition metal
dichalcogenides, in which spin and pseudospin degrees of freedom are locked
together [M. 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\textcolor{black}{{} (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 charge-spin conversion
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.
