The checkerboard modulation and the inter-layer asymmetry of the hole density in cuprates

The 2D pair-condensate is characterized by a charge ordered state with a "checkerboard" pattern in the planes and with an alternating superstructure along the c-axis.We find that Coulomb energy gain occurs along the c-axis, which is proportional to the measured condensation energy and is due to inter-layer charge complementarity (charge asymmetry of the boson condensate. The static c-axis dielectric constant and the in-plane coherence length are also calculated for various cuprates and compared with the available experimental data. We find excellent agreement .