Dirac-fermions in graphene d-wave superconducting heterojunction with the spin orbit interaction

In this study, based on the Dirac-Bogoliubov-de Gennes equation, we theoretically investigate the interaction effect between the anisotropic d-wave pairing symmetry and the spin orbit interaction (the Rashba spin orbit interaction (RSOI) and the Dresselhaus spin orbit interaction (DSOI)) in a graphene superconducting heterojunction. We find that the spin orbit interaction (SOI) plays a critical role on the tunneling conductance in the pristine case, but minimally affecting the tunneling conductance in the heavily doped case. As for the zero bias state, in contrast to the keep intact feature in the heavily doped case, it exhibits a distinct dependence on the RSOI and the DSOI in the pristine case. In particular, the damage of the zero bias state with a slight DSOI results in the disappearance of the zero bias conductance peak. Moreover, the tunneling conductances also show a qualitative difference with respect to the RSOI when both the RSOI and the DSOI are finite. These remarkable results suggest that the SOI and the anisotropic superconducting gap can be regarded as a key tool for diagnosing the specular Andreev reflection.