Unconventional superconducting states of interlayer pairing in bilayer and trilayer graphene

We develop a theory for interlayer pairing of chiral electrons in graphene materials which results in an unconventional superconducting state with an s-wave spin-triplet order parameter. In a pure bilayer graphene, this superconductivity exhibits a gapless property with an exotic effect of temperature-induced condensation causing an increase of the pairing amplitude with increasing temperature. We find that a finite doping opens a gap in the excitation spectrum and weakens this anomalous temperature dependence. We further explore the possibility of realizing a variety of pairing patterns with different topologies of the Fermi surface, by tuning the difference in the doping of the two layers. In trilayer graphene, the interlayer superconductivity is characterized by a two-component order parameter which can be used to define two distinct phases in which only one of the components is nonvanishing. For ABA stacking the stable state is determined by a competition between these two phases. On variation of the relative amplitude of the corresponding coupling strength, a first-order phase transition can occur between these two phases. For ABC stacking, we find that the two phases coexist with the possibility of a similar phase transition, which turns out to be second order. DOI: 10.1103/PhysRevB.86.214503