Flat-band FFLO State from Quantum Geometric Discrepancy

Abstract: We propose a new scheme for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) Cooper pairing states within ultraflat bands. Central to our approach is the concept of "quantum geometric discrepancy" (QGD), which characterizes the discrepancy in the quantum geometry of paired electrons, giving rise to the flat-band FFLO instability. Remarkably, we find that this instability is directly related to a new quantum geometric quantity we term "anomalous quantum distance", which formally captures QGD. To model both QGD and the anomalous quantum distance, we examine a flat-band electronic Hamiltonian with tunable spin-dependent quantum metrics. Utilizing the band-projection method, we analyze the QGD-induced FFLO instability from pair susceptibility near the superconducting critical temperature. Furthermore, we perform self-consistent mean-field calculations to obtain the phase diagram of the BCS-FFLO transition driven by QGD, which aligns well with our analytical results. We emphasize that QGD serves as a distinctive protocol for stabilizing the flat-band FFLO phase.