Possible three-dimensional chiral charge ordered superconducting state in cuprates

The 2D pair-condensate is characterized by a fluctuating chiral charge ordered state with a "checkerboard" pattern in the CuO_2 planes and with an alternating supermodulation along the c-axis in such a way that the adjacent layers are mirror images of one anothers electronic state. Planar chiral order is revealed with a recent circular dichroism (CD) ARPES experiment (A. Kaminski, et al., Nature, 416, 611. (2002)). We propose further CD experiments on ultrathin films with varying thickness and argue that the odd number of unit cells along the c-axis might provide dichroism hence might support the picture of 3D chirality in cuprates. We find that Coulomb energy gain occurs along the c-axis within a multilayer chiral charge ordered state, which is proportional to the measured bilayer condensation energy and to $T_c$ at optimal doping. Within our approach the superconducting (SC) pair is composed of the hole content of the coherence area and the self-repulsion of the condensate is compensated by the gain in the inter-layer Coulomb energy below $T_c$. The SC condensate and the fluctuating charge order can also be described by a dynamical inter-layer electrostatic complementarity.