Pauli limiting and metastability regions of superconducting graphene and intercalated graphite superconductors

Abstract

We present a study of metastability regions in the in-plane magnetic field versus temperature phase diagram of graphene and intercalated graphite superconductors. Due to the vanishing density of states, undoped graphene requires a finite BCS interaction ${V}_{c}$ to become superconducting (any finite doping drives this critical value to zero). Above ${V}_{c}$, superconducting graphene under in-plane magnetic field displays the conventional low temperature first-order transition (FOT) to the normal phase, but the width of the associated metastability region (normalized to the zero-temperature critical field) vanishes when doping goes to zero and the interaction approaches ${V}_{c}$. In the case of intercalated graphite superconductors, modeled as two-dimensional two-band superconductors (a graphene-like band and a metallic interlayer band), a critical graphene intraband interaction is required for the appearance of a second metastability region in the superconducting region of the phase diagram. The width of this metastability region also goes to zero as the graphene intraband interaction approaches, from above, its critical value and the metastability region vanishes at the zero-temperature supercooling field associated with the metallic interlayer band. Slightly above this critical value, the low-temperature FOT line bifurcates at an intermediate temperature into a FOT line and a second-order transition line.