A framework for the description of charge order, pseudo and superconducting gap, critical temperature and pairing interaction in cuprate superconductors.

A unified phenomenological description framework is proposed for the evaluation of some of the most important observables of the cuprate superconductors: the pseudogap (PG) Δ, the local superconducting amplitudes Δ(), the critical temperatureand charge ordering (CO) parameters. Recent detailed measurements of CO structures and CO wavelengthsare faithfully reproduced by solutions of a Cahn-Hilliard differential equation with a free energy potentialthat produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to theamplitude. The local SC amplitude and phaseare connected by Josephson coupling() and the SC long-range order transition occurs whenEJ∼kBTc. The calculated results of the wavelength, Δ,ΔSCandcalculations are in good agreement with a variety of experiments.