Statistics of the cuprate pairon states on a square lattice

Abstract

In this paper the fundamental parameters of high-$T_c$
superconductivity are shown to be connected to the statistics of
pairons on a square lattice. In particular, we study the density
fluctuations and the distribution of Voronoi cell areas surrounding
each pairon on the scale of the antiferromagnetic correlation
length, for the complete range of pairon concentration. We show that
the key parameters of the phase diagram, the $T_c$ dome, and the
pseudogap temperature $T^*$, emerge from the statistical properties
of the pairon disordered state. In this approach, the
superconducting and the pseudogap states appear as inseparable
phenomena. The condensation energy, which fixes the critical
temperature, is directly proportional to the {\it correlation
energy} between pairons and {\it 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 pseudogap 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 BCS mechanism. Our predictions are in quantitative agreement
with low-temperature tunneling and photoemission spectroscopy
experiments.