Spin Hall effect in a curved graphene with spin–orbit interaction

The effect of a curvature in a graphene with a spin–orbit interaction (SOI) is studied using a realistic π and σ orbital tight-binding (TB) model. The coupling of the atomic SOI and the curvature-induced orbital mixing produces an effective Rashba-type SOI and causes the k-dependent energy splitting in the low-energy electronic structure near the K point. We find that the spin Hall effect (SHE) is enhanced by the curvature effect. An effective π orbital model, which includes the SOI and curvature effects perturbatively, is also discussed.