Optimal inhomogeneity for superconductivity: Finite-size studies

Abstract

We report the results of exact-diagonalization studies of Hubbard models on a $4\ifmmode\times\else\texttimes\fi{}4$ square lattice with periodic boundary conditions and various degrees and patterns of inhomogeneity, which are represented by inequivalent hopping integrals $t$ and ${t}^{\ensuremath{'}}$. 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 the order of the bandwidth and intermediate inhomogeneity $0<{t}^{\ensuremath{'}}<t$. The maximum value of the ``pair-binding energy'' we have found with purely repulsive interactions is ${\ensuremath{\Delta}}_{pb}=0.32t$ for the checkerboard Hubbard model with $U=8t$ and ${t}^{\ensuremath{'}}=0.5t$. 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.