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) $Δ_{\rm PG}$, the local superconducting amplitudes $Δ_{\rm SC}(r_i)$, the critical temperature $T_{\rm c}$ and charge ordering (CO) parameters. Recently detailed measurements of CO structures and CO wavelengths $λ_{\rm CO}$ are faithfully reproduced by solutions of a Cahn-Hilliard differential equation with a free energy potential $V_{\rm GL}$ that produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to the $V_{\rm GL}$ amplitude. The local SC amplitude and phase $θ_i$ are connected by Josephson coupling $E_{\rm J}(r_{\rm ij})$ and the SC long-range order transition occurs when ${\left < E_{\rm J} \right>} \sim k_{\rm B}T_{\rm c}$. The calculated results of the wavelength $λ_{\rm CO}$, $Δ_{\rm PG}$, $\left < Δ_{\rm SC}\right >$ and $T_{\rm c}$ calculations are in good agreement with a variety of experiments.

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