Superconductivity in Inhomogeneous Hubbard Models

Abstract

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t^{\prime }$, 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 ({\it 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 $0<U<U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U-U_c|<\mathcal{O}(t^{\prime })$, which gives way to a Fermi liquid phase at large $U>U_c=4.58$.

7 pages, a sign error in Eq.(3) has been corrected and its consequence has been discussed with updated figures