  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.
