Rashba-induced spin Hall response in a disordered $WTe_2$ four-terminal structure

The paramount acumen for controlling spin transport properties in nonmagnetic materials is the usage of spin-orbit coupling (SOC). We propose a model to calculate the spin hall angle (SHA) for the elemental transition metal dichalcogenide compound, $WTe_2$ entrenched on the intrinsic Rashba SOC. This model, is based on the Landauer-Buttiker formalism for quantum transport, and the $4$-terminal device setup with the presence of disorder from random onsite potential fluctuations. The SHA, including the mean and RMS values, also illustrate the mesoscopic oscillations, and the values obtained are $25\%$ and $30\%$, respectively. The variation pattern of charge and spin current, along with the mean and spin Hall conductance, can be a comparative measure for other TMDs and monolayer Xenes. To validate our outcomes, we compare our results with experimental data and numerically extract real-space simulation results based on the nearest-neighbor tight binding (NNTB) model. Also our results are in line with the scaling theory of localization. This work sets the stage to calculate the spin Hall angle and spin Hall conductivity for other elemental monolayer Xenes and TMDs, considering the intrinsic scattering mechanisms. An extension of this work will be to explore the possible spintronics applications for extrinsic scattering, including side-jump and skew-jump scattering processes.