Condensation energy, charge ordering and inter-layer coupling in cuprates

The correlation between the condensation energy and the critical temperature is studied within a charge ordered superlattice bilayer 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 drop of the c-axis dielectric screening can be the primary source of the condensation energy at optimal doping.We find that Coulomb energy gain occurs along the c-axis, which is proportional to the measured condensation energy ($U_0$) and to $T_c$: $E_c^{3D} \approx 2 (\xi_{ab}/a_0+1)^2 U_0 \approx k_B T_c$ and is due to inter-layer charge complementarity (charge asymmetry of the boson condensate)where ${\xi }_{ab}$ is the coherence length of the condensate and $a_0\approx 3.9\mathring{A}$ is the in-plane lattice c onstant.The static c-axis dielectric constant ${ϵ}_c$ is calculated for various cuprates and compared with the available experimental data.