Enhanced pairing in the checkerboard Hubbard ladder

We study the repulsive Hubbard two-leg ladder model with various forms of inhomogeneity using the density matrix renormalization group method. For instance, we consider the case in which the hopping matrix elements $t_{ij}$ are periodically modulated so that the ladder consists of an array of $2\times 2$ plaquettes with couplings $t_{ij}=t$ within a plaquette and $t_{ij}=t' \leq t$ between plaquettes. In this ``checkerboard'' case, both the spin gap and the pair binding energy are maximized for an intermediate value of the inter-plaquette coupling, $t'\sim t/2$. This enhancement of the pairing signatures seems to be special to breaking the ladder into plaquettes, and does not occur for other forms of inhomogeneity which were explored, e.g. a site-centered charge density wave. The Luttinger exponent $K_c$ is found to be nearly independent of the inter-plaquette coupling. For an array of weakly coupled Hubbard ladders, this implies that the superconducting critical temperature T$_c$ can be increased by breaking each ladder into plaquettes.