Quantum-metric effects in flat-band superconductors

We investigate the impacts of the quantum geometry of Bloch states, specifically through the band-resolved quantum-metric tensor, on Cooper pairing and flat-band superconductivity in a three-dimensional pyrochlore-Hubbard model. We establish direct relations between the superfluid weight of a multiband superconductor and (i) the effective mass of the lowest-lying two-body branch at zero temperature, (ii) the kinetic coefficient of the Ginzburg-Landau theory in proximity to the critical temperature Tc, (iii) the velocity of the low-energy Goldstone modes at zero temperature, and (iv) coherence lengths near Tc and at zero temperature.