Numerical study of giant nonlocal resistance in 2D spin orbital coupling system

Recent experiments find the signal of giant nonlocal resistance $R_{NL}$ in H-shaped graphene sample due to the Spin/Valley Hall Effect. Interestingly, compared with the local resistance $R_L$, $R_{NL}$ decreases much more quickly when the Fermi energy deviates from the Dirac point, which does not satisfy the classical relation: $R_{NL} \propto R_L^3$. In this work, we simulate such transport phenomenon in H-shaped graphene based on the non-equilibrium Green function method. Near the Dirac point, there does exist a large nonlocal resistance signal, which exhibits much sharper than the local one. Moreover, we investigate the relationship between $R_L$ and $R_{NL}$, which can be affected by spin-orbital coupling strength, Fermi energy, sample size, etc. At last, we discuss the possible mechanism that leads to the deviation of $R_{NL}$ from classical $R_{NL} \propto R_L^3$.