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

Proximity-induced phenomena in van der Waals heterostructures have emerged as a platform to tailor the electronic, spin, optical, and topological properties in two-dimensional materials. A crucial degree of freedom, which has only recently been recognized, is the relative twist angle between the monolayers. While partial results exist in the literature, we present here a comprehensive first-principles-based investigation of the twist-angle dependent proximity spin-orbit coupling (SOC) in graphene in contact with, or encapsulated by, monolayer transition metal dichalcogenides (TMDCs) MoS2, MoSe2, WS2, and WSe2. Crucially, our commensurate supercells comprise monolayers with strains of less than 2.5%, minimizing band-offset artifacts. We confirm earlier DFT results that for Mo-based TMDCs the proximity valley-Zeeman SOC exhibits a maximum at around 15 degrees -20 degrees and vanishes at 30 degrees for symmetry reasons. Although such a maximum was also predicted by tight binding simulations for W-based TMDCs, we find an almost linear decrease of proximity valley-Zeeman SOC in graphene/WSe2 and graphene/WS2 when twisting from 0 degrees to 30 degrees. We also refine previous DFT simulations and show that the induced Rashba SOC is rather insensitive to twisting, while acquiring a nonzero Rashba phase angle phi which measures the deviation of the electron spin from in-plane transverse direction to the momentum, for twist angles different from 0 degrees and 30 degrees. The Rashba phase angle var phi varies from -20 degrees to 40 degrees, with the largest variation (40 degrees) found for MoS2 at a twist angle of 20 degrees. This finding contradicts earlier tight-binding predictions that the Rashba angle can be 90 degrees in the studied systems. In addition, we study the influence of a transverse electric field, vertical and lateral shifts, and TMDC encapsulation on the proximity SOC for selected twist angles. Within our investigated electric field limits of +/- 2 V/nm, mainly the Rashba SOC can be tuned by about 50%. The interlayer distance provides a giant tunability, since the proximity-induced SOC can be increased by a factor of 2-3, when reducing the distance by only about 10%. When encapsulating graphene between two TMDCs, both twist angles are important to control the interference of the individual proximity-induced SOCs, allowing to precisely tailor the proximity-induced valley-Zeeman SOC in graphene, while the Rashba SOC becomes suppressed. Finally, based on our effective Hamiltonians with fitted parameters to low-energy ab initio band structures, we calculate experimentally measurable quantities such as spin lifetime anisotropy and charge-to-spin conversion efficiencies. The spin lifetime anisotropy-being the ratio between out-of-plane and in-plane spin lifetimes-can become giant (up to 100), depending on the TMDC, twist angle, transverse electric field, and the interlayer distance. The charge-to-spin conversion can be divided into three components which are due to spin-Hall and Rashba-Edelstein effects with nonequilibrium spin-density polarizations that are perpendicular and parallel to the applied charge current. All conversion efficiencies are highly tunable by the twist angle and the Fermi level.