Pair condensation and inter-layer coupling in cuprates: pairing on a superlattice

We analyze the superconducting state and the c-axis charge dynamics of cuprates using a charged ordered bilayer superlattice model in which pairing is supported by inter-layer Coulomb energy gain. The superlattice nature of high temperature superconductivity is experimentally suggested by the smallness of the coherent length \xi = 10 to 30 A which is comparable with a width of a 4X4 to 8X8 square supercell lattice layer. The temperature induced 2D-3D quantum phase transition of the hole-content is also studied. Pair condensation leads to the sharp decrease of the normal state c-axis anisotropy of the hole-content and reduces inter-layer dielectric screening. The decrease of the c-axis dielectric screening can be the primary source of the condensation energy. The 2D pair condensate can be characterized by a charge ordered state with a "checkboard" pattern seen by scanning tunneling microscopy.