Strong repulsive interactions and potential inhomogeneities both tend to localize Fermions on a lattice and lead to loss of superconductivity. The natural question that comes up is whether they compete or complement each other when both are present in a system at the same time. In this talk we will use an effective Hamiltonian approach which treats both interactions and inhomogeneities on the same footing to look at two systems: (a) the Ionic Hubbard Model at half-filling, where a staggered potential on a bipartite lattice competes with interactions to delocalize charge and give birth to a novel superconductors. The superconducting Tc scales with the bandwidth of the system and shows a non-monotonic behaviour with staggered potential, (b) the disordered Hubbard model away from half-filling, where weak disorder competes with strong interactions to preserve superconductivity, but strong disorder complements interactions leading to sudden death of superconductivity in this system.
