Coupled spin and valley Hall effects driven by coherent tunneling

We predict the coexistence of tunneling spin and valley Hall effects when electrons in graphene coherently transmit through a barrier with the broken inversion symmetry and proximity-induced spin-orbit coupling. Due to the rotation of the pseudospin in the tunneling process, the transmitted electrons acquire a finite spin- and valley-dependent backreflection geometric phase when the two interfaces of the barrier are asymmetric. This results in a spin- and valley-dependent skew coherent tunneling, which is responsible for the transverse spin and valley Hall currents. We further demonstrate that the coherent-tunneling assisted charge-spin and charge-valley conversions are highly efficient with large Hall angles. Our work provides a new route for the generation of efficient spin and valley Hall effects, suggesting potential applications for spintronic and valleytronic devices.