Optimal inhomogeneity for superconductivity

We study the effect of nonuniform transverse couplings on a quasi-one-dimensional superconductor. We show that inhomogeneous couplings quite generally increase the superconducting (pairing) gap relative to the uniform system, but that beyond an optimal degree of inhomogeneity, they lead to a suppression of the tendency towards phase coherence. The optimal conditions for superconductivity are derived. We also show that a delocalized, spin-gapped phase is stable against weak disorder in a four-leg ladder with moderate repulsive interactions.