Quantum metric driven transition between superfluid and incoherent fluid

Flat band superfluidity is a prototypical strongly correlated problem, which attracts a lot attention recently. Given the quenched kinetic energy in flat band systems, special attention is paid to the role of wavefunctions and quantum geometric tensor.

In this work, we study the stability of flat band superfluidity under the interplay between repulsive interaction and quantum metric (or quantum mechanical wavefunctions). We consider spatially indirect excitons in the Lieb lattice bilayer as an example. We show that due to the presence of repulsive interaction, the excitons may form an incoherent fluid. By increasing the quantum metric, the exciton fluid experiences a transition into the superfluid phase. Such transition may be captured by a model of Josephson junction array, which is beyond mean field description.