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_PG, the local superconducting amplitudes Δ_SC(r _i), the critical temperature T _c and charge ordering (CO) parameters. Recent detailed measurements of CO structures and CO wavelengths λ _CO are faithfully reproduced by solutions of a Cahn–Hilliard differential equation with a free energy potential V _GL that produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to the V _GL amplitude. The local SC amplitude and phase θ _i are connected by Josephson coupling E _J(r _ij) and the SC long-range order transition occurs when $⟨E_{\text{J}}⟩\sim k_{\text{B}}{T}_{\text{c}}$. The calculated results of the wavelength λ _CO, Δ_PG, $⟨{\Delta }_{\text{SC}}⟩$ and T _c calculations are in good agreement with a variety of experiments. (letter)