We investigate, using first-principles methods and effective-model simulations, the spin-orbit coupling proximity effects in a bilayer heterostructure comprising phosphorene and ${\mathrm{WSe}}_2$ monolayers. We specifically analyze holes in phosphorene around the $\mathrm{\Gamma }$ point, at which we find a significant increase of the spin-orbit coupling that can be attributed to the strong hybridization of phosphorene with the ${\mathrm{WSe}}_2$ bands. We also propose an effective spin-orbit model based on the ${\mathbf{C}}_{1\mathrm{v}}$ symmetry of the studied heterostructure. The corresponding spin-orbit field can be divided into two parts: the in-plane field, present due to the broken nonsymmorphic horizontal glide mirror plane symmetry, and the dominant out-of-plane field triggered by breaking the out-of-plane rotational symmetry of the phosphorene monolayer. Furthermore, we also demonstrate that a heterostructure with ${60}^{\circ }$ twist angle exhibits an opposite out-of-plane spin-orbit field, indicating that the coupling can effectively be tuned by twisting. The studied phosphorene/${\mathrm{WSe}}_2$ bilayer is a prototypical low common-symmetry heterostructure in which the proximity effect can be used to engineer the spin texture of the desired material.

• Received 23 June 2023
• Revised 25 August 2023
• Accepted 13 September 2023

DOI:https://doi.org/10.1103/PhysRevB.108.115311