Work supported in part by US Department of Energy contract DE-AC02-76SF00515. Superconductivity in Inhomogeneous Hubbard Models

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, t, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters (e.g. the effective mass) which are smooth functions of the Hubbard interaction, U . By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, d-BEC) for 0 < U < Uc, which smoothly crosses over to an intermediate BCS-like superconducting phase (d-BCS), also with no nodal quasi-particles, for |U − Uc| < O(t), which gives way to a Fermi liquid phase at large U > Uc = 4.58.