Flat-band Fulde-Ferrell-Larkin-Ovchinnikov state from quantum geometric discrepancy

Abstract We propose a new scheme for realizing Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) Cooper pairing states within flat bands, in contrast to the conventional paradigm such as the Zeeman effect. Central to our scheme is the concept of “quantum geometric discrepancy” (QGD) that measures differences in the quantum geometry of paired electrons and drives the flat-band FFLO instability. Remarkably, we find that this instability is directly related to a quantum geometric quantity known as “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 pairing susceptibility. Furthermore, we perform mean-field numerical simulations to obtain the phase diagram of the BCS-FFLO transition, which aligns well with our analytical results. Our work demonstrates that QGD offers a general and distinctive mechanism for stabilizing the flat-band FFLO phase.