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Relativistic model for electron-hole pairing in the superconducting state of graphene-based materials

We propose a graphene-based model for realizing a new type of gapless condensate by pairing of electron-like (n) carriers of a Dirac cone conduction band with hole-like (p) carriers of a Dirac valance band. Ferromagnetic superconductivity (FS) in monolayer graphene or pairing between oppositely (n and p) doped layers of a double layer graphene allow for the formation of this p-n superconductivity. For FS in graphene, the p-n condensate dominates the zero temperature phase diagram at low levels of doping and high exchange fields. We show that p-n pairing with p+ip-wave symmetry presents a stable condensate phase, which can cover the phase diagram up to surprisingly strong exchange fields. Our study reveals that the characteristics of relativistic quantum physics affect the interplay between ferromagnetic ordering and superconductivity in a fundamental way.