Superconductivity in a topological lattice model with purely-repulsive strong interactions

We present numerical evidence for superconductivity in a microscopic model with purely-repulsive strong interactions. In particular, we propose and investigate a spinful bilayer system of quarter-flux Hofstadter lattices subjected to opposite magnetic fields, equipped with both local Hubbard interactions and inter-layer tunneling. The underlying band structure possesses nearly flat Chern bands related by time-reversal symmetry and possesses $w_2$ fragile topology, much like the flat bands of magic angle bilayer graphene. At integer filling, strong interactions give rise to flavor-polarized insulating states analogous to quantum Hall ferromagnets. Employing the infinite density matrix renormalization group method on a variety of cylinder circumferences, we find striking numerical evidence for $p$-wave superconductivity upon lightly hole-doping a family of these insulators. We conclude by providing a theoretical understanding of the superconducting instability and outlining a potential experimental implementation in an optical lattice.