Pairing in magic-angle twisted bilayer graphene: Role of phonon and plasmon umklapp

Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by strong interactions relative to electronic bandwidth, its single-particle properties are unique and likely play important role some of phenomenological complexity. Some salient features include bandwidth smaller than characteristic phonon non-trivial structure underlying Bloch wavefunctions. We perform theoretical study cooperative effects due phonons plasmons on pairing order disentangle distinct played these modes superconductivity. consider variant with enlarged number fermion flavors, $N \gg 1$, where instabilities reduces conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving mini-optical modes, which arise physically as result folding original acoustic branch moir\'e superlattice structure, contribute significantly towards enhancing pairing. also investigate dynamics screened Coulomb interaction pairing, leads enhancement narrow window fillings, effect external screening metallic gate At coupling dynamical leaves spectral mark single particle tunneling density states. thus predict such will appear at specific frequencies corresponding sound velocity times integer multiple Brillouin zone size.