Kekul\'e Superconductivity in Twisted Magic Angle Bilayer Graphene

While it has been one of the most important new physics discoveries in the last decade, the nature of superconductivity in the twisted graphene family remains an unsolved problem. Motivated by recent scanning tunneling experiments that report Kekul'e ordering in moir'e graphene superconductors, we develop a microscopic theory of this superconductivity for the twisted bilayer system. The pairing we find is an intra-valley, finite-momentum pair-density wave (PDW) that intrinsically carries a Kekul'e modulation. This state exhibits three salient features: (i) spontaneous breaking of $C_3$ rotation symmetry, producing nematic order; (ii) an anomalously large gap to critical-temperature ratio $\Delta/T_c$; and (iii) a quasiparticle density of states that evolves from a V-shaped profile to a fully gapped, U-shaped spectrum as the attraction increases which is accompanied by systematic behavior of the temperature dependent zero bias conductance. These features align with key experimental signatures. We find, as well, that with only modest interaction strengths, the state is near to a BEC-like phase, consistent with the observed extremely short coherence lengths. Taken together, these results identify a microscopic intra-valley Kekul'e PDW as a compelling candidate for unconventional superconductivity in the twisted graphene family.