Interplay of valley hall effect and spin hall effect in strained graphene

Abstract

Graphene subject to fairly modest strain levels can sustain VHE. In addition, if the impurities also induce Kane-Mele spin-orbit coupling, such functionalized graphene will exhibit an extrinsic spin Hall effect (SHE). Under such conditions, We develop a minimal model to study the interplay of spin and valley Hall effects, which leads to the competition of spin and valley Hall currents and the emergence of a longitudinal neutral spin-valley current. We uncover two anomalous behaviors in the nonlocal transport. Firstly, Hanle effect can be weakened or removed by the fairly modest strain, due to the competition of spin and valley Hall currents. Secondly, a narrow oscillating signals can be dramatically enhanced by resonance in small magnetic field for comparable spin and valley relaxation, as a result of the longitudinal spin-valley current. The remarkable feature of this narrow oscillation is that the resonant magnetic field is quite robust to the change of strain and distance. Both behaviors should be observable in strained graphene decorated with adatoms inducing local spin-orbit coupling, and may shield light on the existing experimental controversies concerning the origin of the non-local signals.