Enhanced Kohn-Luttinger superconductivity in geometric bands

We study the effect of the electron wavefunction on Kohn-Luttinger superconductivity. The role of the wavefunction is encoded in a complex form factor describing the topology and geometry of the bands. We show that the wavefunction significantly impacts the superconducting transition temperature and superconducting order parameter. We illustrate this using the lowest Landau level form factor and find exponential enhancement of Tc for the resulting topological superconductor. This enhancement of Tc is due to the resonance between the Berry flux enclosed by the Fermi surface and Cooper pair angular momentum.} We find that the ideal band geometry, which favors a fractional Chern insulator in the flat band limit, has an optimal Tc. Finally, we apply this understanding to a model relevant to rhombohedral graphene multilayers and unravel the importance of the band geometry for achieving robust superconductivity.