Superconductivity, pseudogap, and phase separation in topological flat bands

Superconductivity (SC) is a macroscopic quantum phenomenon that requires electron pairs to delocalize over large distances. A long-standing question is whether SC can exist even if the electrons' kinetic energy is completely quenched, as is the case in a flat band. This is fundamentally a non-perturbative problem since the interaction energy scale is the only relevant energy scale, and hence it requires going beyond the traditional perturbative BCS theory of SC. We study a 2D model of an isolated narrow band at partial filling with local attractive interactions, using quantum Monte Carlo calculations. We focus on topologically non-trivial flat bands where the single-particle wavefunctions that span these bands cannot be completely spatially localized. Our calculations unambiguously show that the ground state is a superconductor; strikingly, the critical temperature scales nearly linearly with the interaction strength. Above the SC transition temperature, we find a broad pseudogap regime that exhibits strong pairing fluctuations and a tendency towards electronic phase separation. Weak nearest neighbor attraction suppresses SC entirely and drives the system to phase separate. We discuss the possible relevance of SC in this unusual regime to the physics of flat band moire materials.