Superconductivity of repulsive spinless fermions with sublattice potentials

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two can exhibit $d$-wave $f$-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the lattice displays a much richer phase diagram including topological $p+ip$ which is induced by qualitatively different mechanism compared to pairing. illuminate this several complementary perspectives: analytically perform projection analyze continuum low-energy description we numerically calculate binding energies for pair larger bound states few-body near half filling. Furthermore, finite present diagrams based extensive functional renormalization group density matrix calculations.