The Optimal Inhomogeneity for Superconductivity: Finite Size Studies

Abstract

We report the results of exact diagonalization studies of Hubbard models on a $4\times 4$ 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 ${\Delta }_{pb}=0.32t$ 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.

8 pages, 9 figures; minor revisions; more references added

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