Determining proximity-induced spin–orbit coupling in graphene via spin-conserving resonant tunneling

Graphene acquires substantial spin–orbit coupling (SOC) via the proximity effect to transition-metal dichalcogenides. The induced SOC consists mainly of two components: the Valley-Zeeman type, which produces out-of-plane spin polarization, and the Rashba type, which generates an in-plane vortex-like spin texture. Their relative strengths are predicted to vary with the twist angle θₚᵣₒₓ between graphene and WSe₂. Here, we investigate the proximity-induced SOC terms and their dependence on the twist angle by measuring spin-conserving resonant tunneling between two proximitized graphene layers.

We fabricated graphene/WSe₂/graphene junctions, where WSe₂ serves both as a tunneling barrier and as a source of SOC for the adjacent graphene layers. For a graphene/WSe₂ junctions with θₚᵣₒₓ = 18°, the conductance peak associated with resonant tunneling splits into two distinct peaks, whereas for θₚᵣₒₓ = 30°, no splitting is observed. Comparison with theoretical modeling indicates that the splitting occurs when the pair of eigenstates involved in tunneling have spins aligned out-of-plane, while its absence corresponds to in-plane spin alignment. These findings demonstrate that Valley-Zeeman SOC dominates at θₚᵣₒₓ = 18°, whereas Rashba SOC dominates at θₚᵣₒₓ = 30°.