Many-Body Superconductivity in Topological Flat Bands

In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states and density excitations obey an effective single-particle Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum metric. The rest of the bound state spectrum is classified by topological quantum chemistry, which we use to identify Cooper pairs with Weyl nodes, higher angular momentum pairing, and fragile topology. We also add electron kinetic energy as a perturbation to show that the strongest pairing occurs at half filling and not at the highest density of states. This is similar in spirit to the superconductivity observed in twisted bilayer graphene.