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Twist- and gate-tunable proximity spin-orbit coupling, spin relaxation anisotropy, and charge-to-spin conversion in heterostructures of graphene and transition-metal dichalcogenides

We present a DFT-based investigation of the twist-angle dependent proximity spin-orbit coupling (SOC) in graphene/TMDC structures. We find that for Mo-based TMDCs the proximity valley-Zeeman SOC exhibits a maximum at around 15--20°, and vanishes at 30°, while for W-based TMDCs we find an almost linear decrease of proximity valley-Zeeman SOC when twisting from 0° to 30°. The induced Rashba SOC is rather insensitive to twisting, while acquiring a nonzero Rashba phase angle, $φ\in [-20;40]$°, for twist angles different from 0° and 30°. This finding contradicts earlier tight-binding predictions that the Rashba angle can be 90° in the studied systems. In addition, we study the influence of several tunability knobs on the proximity SOC for selected twist angles. By applying a transverse electric field in the limits of $\pm 2$ V/nm, mainly the Rashba SOC can be tuned by about 50\%. The interlayer distance provides a giant tunability, since the proximity SOC can be increased by a factor of 2--3, when reducing the distance by about 10\%. Encapsulating graphene between two TMDCs, both twist angles are important to control the interference of the individual proximity SOCs, allowing to precisely tailor the valley-Zeeman SOC in graphene, while the Rashba SOC becomes suppressed. Finally, based on our effective Hamiltonians with fitted parameters, we calculate experimentally measurable quantities such as spin lifetime anisotropy and charge-to-spin conversion efficiencies. The spin lifetime anisotropy can become giant, up to $10^4$, in encapsulated structures. The charge-to-spin conversion, which is due to spin-Hall and Rashba-Edelstein effects, can lead to twist-tunable non-equilibrium spin-density polarizations that are perpendicular and parallel to the applied charge current.