Statistics of the cuprate pairon states on a square lattice

Abstract

In this paper the fundamental parameters of high-Tc superconductivity are shown to be connected to the statistics of pairons (hole pairs in their antiferromagnetic (AF) environment) on a square lattice. In particular, we study the density fluctuations and the distribution of the area surrounding each pairon on the scale of the AF correlation length , for the complete range of hole concentration. We show that the key parameters of the phase diagram, the Tc dome, and the pseudogap (PG) temperature , emerge from the statistical properties of the pairon disordered state. In this approach, the superconducting and the PG states appear as inseparable phenomena. The condensation energy, which fixes the critical temperature, is directly proportional to the correlation energy between pairons and not to the energy gap, contrary to conventional superconductors. When the correlation energy between pairons is suppressed by fluctuations, either thermally, by disorder, or in the vortex core, the PG state of disordered pairons is obtained. We attribute the unique features of cuprate superconductivity to this order–disorder transition in real space, which clearly differs from the Bardeen–Cooper–Schrieffer mechanism. Our predictions are in quantitative agreement with low-temperature tunneling and photoemission spectroscopy experiments.