Proximity Effects in Bilayer Graphene on Monolayer WSe_{2}: Field-Effect Spin Valley Locking, Spin-Orbit Valve, and Spin Transistor.

Proximity orbital and spin-orbit effects of bilayer graphene on monolayer WSe_{2} are investigated from first principles. We find that the built-in electric field induces an orbital band gap of about 10 meV in bilayer graphene. Remarkably, the proximity spin-orbit splitting for holes is 2 orders of magnitude-the spin-orbit splitting of the valence band at K is about 2 meV-more than for electrons. Effectively, holes experience spin valley locking due to the strong proximity of the lower graphene layer to WSe_{2}. However, applying an external transverse electric field of some 1  V/nm, countering the built-in field of the heterostructure, completely reverses this effect and allows, instead of holes, electrons to be spin valley locked with 2 meV spin-orbit splitting. Such a behavior constitutes a highly efficient field-effect spin-orbit valve, making bilayer graphene on WSe_{2} a potential platform for a field-effect spin transistor.