The Optimal Inhomogeneity for Superconductivity: Finite Size Studies
We report the results of exact diagonalization studies of Hubbard models on a 4 x 4 square lattice with periodic boundary conditions and various degrees and patterns of inhomogeneity, which are represented by inequivalent hopping integrals t and t{prime}. We focus primarily on two patterns, the checkerboard and the striped cases, for a large range of values of the on-site repulsion U and doped hole concentration, x. We present evidence that superconductivity is strongest for U of order the bandwidth, and intermediate inhomogeneity, 0 < t{prime} < t. The maximum value of the 'pair-binding energy' we have found with purely repulsive interactions is {Delta}{sub pb} = 0.32t for the checkerboard Hubbard model with U = 8t and t{prime} = 0.5t. Moreover, for near optimal values, our results are insensitive to changes in boundary conditions, suggesting that the correlation length is sufficiently short that finite size effects are already unimportant.