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Numerical study of the giant nonlocal resistance in spin-orbital coupled graphene

Recent experiments find the signal of giant nonlocal resistance $R_{NL}$ in H-shaped graphene samples due to the spin/valley Hall effect. Interestingly, when the Fermi energy deviates from the Dirac point, $R_{NL}$ decreases to zero much more rapidly compared with the local resistance $R_L$, and the well-known relation of $R_{NL}\propto R_L^3$ is not satisfied. In this work, based on the non-equilibrium Green's function method, we explain such transport phenomena in the H-shaped graphene with Rashba spin-orbit coupling. When the Fermi energy is near the Dirac point, the nonlocal resistance is considerably large and is much sharper than the local one. Moreover, the relationship between the Rashba effect and the fast decay of $R_{NL}$ compared with $R_L$ is further investigated. We find that the Rashba effect does not contribute not only to the fast decay but also to the peak of $R_{NL}$ itself. Actually, it is the extremely small density of states near the Dirac point that leads to the large peak of $R_{NL}$, while the fast decay results from the quasi-ballistic mechanism. Finally, we revise the classic formula $R_{NL}\propto R_L^3$ by replacing $R_{NL}$ with $R_{Hall}$, which represents the nonlocal resistance merely caused by the spin Hall effect, and the relation holds well.