Coherence length and quantum geometry in a dilute flat-band superconductor

To explore the influence of quantum-geometric effects on the Ginzburg-Landau coherence length in a dilute flat-band superconductor, we adopt a BCS-BEC crossover approach to the multiband pyrochlore-Hubbard model near the critical temperature for superconductivity. Our self-consistent formulation for this three-dimensional lattice benchmarks very well against the so-called zero-temperature coherence length, demonstrating the monotonic decay of the coherence length to zero as the interaction strength increases. Additionally, we show that the effective mass of the many-body bound states (i.e., Cooper pairs) is nearly identical to that of the lowest-lying two-body bound states in the dilute flat-band limit.