Charge ordering and inter-layer coupling in cuprates

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We analyze the superconducting state and c-axis charge dynamics of cuprates at optimal doping using a charge ordered bilayer superlattice model in which pairing is supported by inter-layer Coulomb energy gain (potential energy driven superconductivity).The 2D pair-condensate can be characterized by a charge ordered state with a "checkerboard" like pattern seen by scanning tunneling microscopy.The pair condensation might lead to the sharp decrease of the normal state c-axis anisotropy of the hole content and hence to the decrease of inter-layer dielectric screening.The decrease of the c-axis dielectric screening can be the primary source of the condensation energy below Tc. We find that a net gain in the electrostatic energy occurs along the c-axis, which is proportional to the measured condensation energy (U₀) and with Tc:Ec³ᵈ ≈ 2 (ξab/a₀+1)² U₀ ≈ kB Tc and is due to inter-layer charge complementarity (charge asymmetry of the boson condensate) where ξab is the coherence length of the condensate and a₀ ≈ 3.9 Å is the in-planelattice constant.