Quantum geometric effect on Fulde-Ferrell-Larkin-Ovchinnikov superconductivity

Quantum geometry characterizes the geometric properties of Bloch electrons in the wave space, represented by the quantum metric and the Berry curvature. Recent studies have revealed that the quantum geometry plays a major role in various physical phenomena, from multipole to non-Hermitian physics. For superconductors, the quantum geometry is clarified to appear in the superfluid weight, an essential quantity of superconductivity. Although the superfluid weight was considered to be determined by the Fermi-liquid contribution for a long time, the geometric contribution is not negligible in some superconductors such as artificial flat-band systems and monolayer FeSe. While the superfluid weight is essential for many superconducting phenomena related to the center of mass momenta of Cooper pairs (CMMCP), the full scope of the quantum geometric effect on superconductivity remains unresolved. In this paper, we study the quantum geometric effect on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state acquiring a finite CMMCP in equilibrium. As a benchmark, the phase diagrams of effective models for monolayer FeSe in an in-plane magnetic field are calculated. In the case of the isotropic $s$-wave pairing, the quantum geometry stabilizes the BCS state, and a metastable BCS state appears in the high magnetic field region. In addition, the quantum geometry induces the phase transition from the FFLO state to the BCS state with increasing temperature. On the other hand, for the inter-sublattice pairing, the quantum geometry gives a negative contribution to the superfluid weight; this can induce the FFLO superconductivity in particular parameter sets.