Quantum geometric effects on BCS-BEC crossover in a non-s wave superconductor: Application to magic-angle twisted multilayer Graphene

Recent experiments on magic-angle twisted multilayer Graphene (MATMG) suggest that the superconductivity observed is associated with both an ultrashort coherence length and superconducting gap nodes. The former hints that BCS-BEC crossover could play a key role. The latter requires a deeper understanding of BCS-BEC crossover for a non-s wave superconductor. Experience with $d$-wave pairing in the cuprates shows that pair localization arising from the extended size of the pairs can lead to destruction of the superconducting state at stronger coupling. In MATMG, pair localization is well known to be problematic for an altogether different reason: the underlying normal state energy band structure involves flat energy bands. Importantly, in these systems quantum geometry associated with multi-orbital physics has been shown to be vital for stabilizing two-dimensional s-wave superconductivity. This leads us to present a theory of non-s wave BCS-BEC crossover with both nontrivial quantum geometry and flat energy bands. Our work clarifies the role of quantum geometry on both the Cooper pair mass and condensation temperature for this nodal superconductor across the BCS-BEC spectrum. Related experimental consequences for MATMG are discussed.