Cooper pairing, flat-band superconductivity, and quantum geometry in the pyrochlore-Hubbard model

Abstract

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 pyrochloreHubbard model. First we analyze the low-lying two -body spectrum exactly, and show that the pairing order parameter is uniform in this four -band lattice. This allows us to 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, and (iii) the velocity of the low -energy Goldstone modes at zero temperature. Furthermore, we perform a comprehensive numerical analysis of the superfluid weight and Goldstone modes, exploring both their conventional and geometric components at zero temperature.