Andreev levels in a graphene–superconductor surface

In order to consider the Dirac-like spectrum of graphene we employ the Bogoliubov de Gennes–Dirac formalism to determine the quasiparticle Andreev levels in an NS surface (normal–superconductor). The normal region is characterized by a width L while the superconducting region is semi-infinite and both regions are made of doped graphene. The quasiparticle energy spectrum is originated by the Andreev reflections that occur in the NS interface. It is shown that this spectrum depends on the width of the normal region and the Fermi energy in each region. When the Fermi energy in the normal metal is lower than the gap of the superconductor region, the spectrum is affected by specular Andreev reflections. The equation that is obtained to find the spectrum is very general and we solve it for some particular cases. We find that the energy spectrum oscillates when the Fermi energy in graphene is changed. Finally we obtain under some approximations an equation for the energy spectrum which is similar in structure as those obtained for an INS conventional junction.