English: Left: Dispersion relation of graphene with the conduction band shown by the solid red line and the valence band shown by the dotted blue line. Middle: Dispersion relation for positive energies of graphene coupled to a superconductor at finite positive Fermi energy at ${\displaystyle \Delta =0}$ and ${\displaystyle U=0}$. The solid red and blue lines correspond to the electron and holes from the conducting band. The dotted blue lines correspond to the holes from the valence band. Right: Dispersion relation in the case of zero Fermi energy.