Tunneling conductance of the s-wave and d-wave pairing superconductive graphene–normal graphene junction

Abstract

Within the framework of the Blonder–Tinkham–Klapwijk formalism we calculate and analyze the conductance of the normal graphene — s-wave and independently d-wave pairing superconductive graphene junction. The eigenfunctions, the Andreev and the normal reflection rates are obtained by solving the Dirac–Bogoliubov–de Gennes equations. The Fermi velocity is believed to be different in the normal and in the superconductive regions. We consider the options of gapless and gapped graphene for both cases: s-wave and independently d-wave pairing. It is demonstrated that the characteristics of the junction considered are sensitive to the ratio vFN/vFS where vFN, vFS are the Fermi velocities in the normal and the superconductive graphene respectively. This conclusion refers to the Andreev reflection as well as to the normal one. The first of them is shown to be the dominant process for the formation of the conductivity. These results are true for an arbitrary value of the orientational angle of the d-waves. Each of four cases considered: s-, d-wave pairing and gapless and gapped graphene displays its own specific features of the conductance. The dependence of the conductance on the external electrostatic potential as well as on the Fermi energy is also analyzed in every case. The obtained results may be useful for controlling the transport properties of the normal graphene–superconductive graphene junction.