I want to generalize BdG equation in order to compute the conductance of a junction of graphene with a metal superconductor. The previous works done until now on this hetrojunction is devotted to use proximity induced superconductivity on the graphene sheet. So both side of junctions are governed by Dirac equation. The question arises is that: when a metal is conducted to a graphene sheet directly, in a normal graphene side, because of 2*2 Dirac Hamiltonian the resulted BdG equation have a 4 component spinor just like the Beenakker result C. W. J. Beenakker, Physical Review Letters 97, 067007 (2006).

But from the other side, where a superconductor with Schrodinger like Hamiltonian is placed, we have a two components spinor for quasi particle excitations. So I don't know what should I do about boundary conditions of this wave function in order to compute the conductance of junctions.

I want to generalize BdG equation in order to compute the conductance of a junction of graphene with a metal superconductor. The previous works done until now on this hetrojunction is devotted to use proximity induced superconductivity on the graphene sheet. So both side of junctions are governed by Dirac equation. The question arises is that: when a metal is conducted to a graphene sheet directly, in a normal graphene side, because of 2*2 Dirac Hamiltonian the resulted BdG equation have a 4 component spinor just like the Beenakker's result C. W. J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006) / arXiv:cond-mat/0604594

But from the other side, where a superconductor with Schrodinger like Hamiltonian is placed, we have a two components spinor for quasi particle excitations. So I don't know what should I do about boundary conditions of this wave function in order to compute the conductance of junctions.