Sublattice model of atomic scale pairing inhomogeneity in a   superconductor
  We study a toy model for a superconductor on a bipartite lattice, where intrinsic pairing inhomogeneity is produced by two different coupling constants on the sublattices. The simplicity of the model allows for analytic solutions and tests of the consequences of atomic-scale variations in pairing interactions which have been considered recently in the cuprates. We present results for the transition temperature, density of states, and thermodynamics of the system over a phase diagram in the plane of two pairing coupling constants. For coupling constants of alternating sign, a gapless superconducting state is stable. Inhomogeneity is generally found to enhance the critical temperature, and at the same time the superfluid density is remarkably robust: at T=0, it is suppressed only in the gapless phase. 
Vivek Mishra, P. J. Hirschfeld, and Yu. S. Barash