  In flat bands, superconductivity can lead to surprising transport effects.
The superfluid "mobility", in the form of the superfluid weight $D_s$, does not
draw from the curvature of the band but has a purely band-geometric origin. In
a mean-field description, a non-zero Chern number or fragile topology sets a
lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless
mechanism, might explain the relatively high superconducting transition
temperature measured in magic-angle twisted bilayer graphene (MATBG). For
fragile topology, relevant for the bilayer system, the fate of this bound for
finite temperature and beyond the mean-field approximation remained, however,
unclear. Here, we use numerically exact Monte Carlo simulations to study an
attractive Hubbard model in flat bands with topological properties akin to
those of MATBG. We find a superconducting phase transition with a critical
temperature that scales linearly with the interaction strength. We then
investigate the robustness of the superconducting state to the addition of
trivial bands that may or may not trivialize the fragile topology. Our results
substantiate the validity of the topological bound beyond the mean-field regime
and further stress the importance of fragile topology for flat-band
superconductivity.
