Superfluid weight in Chern bands under a magnetic field

Superconductivity arising out of flat bands in time-reversal invariant systems is thought to be protected by the band’s quantum geometry, providing a lower bound on the superfluid weight which sets the energy scale for phase fluctuations and is responsible for the Meissner effect and persistent supercurrents. We study the superfluid weight for Cooper pairs formed from Landau levels (LLs), which are flat and have non-trivial quantum geometry, using self-consistent mean-field theory. We discuss the evolution of the superfluid weight under the application of a potential, that pins the vortices which are present due to the applied magnetic field, and induces dispersion in the LLs. We examine the evolution of the conventional and geometrical contributions to the superfluid weight. We also investigate the superfluid weight in LL-like bands arising from a topologically nontrivial system exposed to a magnetic field.