Phase transitions to dipolar clusters and charge density waves in high Tc superconductors

We show that doping of hole charge carriers leads to formation of electric dipolar clusters in cuprates. They are created by many body interactions between the dopant ion outside and holes inside the CuO planes. Because of the two-fold degeneracy holes in the CuO plane cluster into four-particles resonance valence bond plaquettes bound with dopant ions. Such dipoles may order into charge-density waves (CDW) or stripes or form a disordered state depending on doping and temperature. The lowest energy of the ordered system corresponds to a local anti-ferroelectric ordering. The mobility of individual disordered dipoles is very low at low temperatures and they prefer first to bind into dipole-dipole pairs. Electromagnetic radiation interacts strongly with electric dipoles and when the sample is subjected to it the mobility changes significantly. This leads to a fractal growth of dipolar clusters. The existence of electric dipoles and CDW induce two phase transitions with increasing temperature, melting of the ordered state and disappearance of the dipolar state. Ferroelectricity at low doping is a natural consequence of such dipole moments. We develop a theory based on two-level systems and dipole-dipole interaction to explain the behavior of the polarization as a function of temperature and electric field