Tuning proximity spin-orbit coupling in graphene/NbSe${}_2$ heterostructures via twist angle

Abstract

We investigate the effect of the twist angle on the proximity spin-orbit coupling (SOC) in graphene/NbSe${}_2$ heterostructures from first principles. The low-energy Dirac bands of several different commensurate twisted supercells are fitted to a model Hamiltonian, allowing us to study the twist-angle dependency of the SOC in detail. We predict that the magnitude of the Rashba SOC can triple, when going from $\hat{I}˜=0^{\circ }$ to $\hat{I}˜=30^{\circ }$ twist angle. Furthermore, at a twist angle of $\hat{I}˜\approx 23^{\circ }$ the in-plane spin texture acquires a large radial component, corresponding to a Rashba angle of up to $\hat{I}¦=25^{\circ }$. The twist-angle dependence of the extracted proximity SOC is explained by analyzing the orbital decomposition of the Dirac states to reveal with which NbSe${}_2$ bands they hybridize strongest. Finally, we employ a Kubo formula to evaluate the efficiency of conventional and unconventional charge-to-spin conversion in the studied heterostructures.