The Superconducting Gap in Weak to Strong Coupling Regime for High-T_c Superconductors.

The behavior of high-temperature superconducting gap in the various coupling regimes has been studied with the help of polaron Green's functions, developed via many-body quantum dynamics by a Hamiltonian that encompasses the contributions of electron, phonon, anharmonicities and impurities. The renormalized energies, energy line widths & shifts are described for polarons followed by the derivation of polaron density of states and superconducting gap equation. The developed gap equation is observed as the function of temperature, Fermi energy, and renormalized electron and phonon energy. The La_2-xSr_xCuO₄ HTS has been hired for numerical analysis. The theory successfully explains the spectacular behavior of the superconducting gap in HTS. The temperature variation of the gap equation is found to be in good agreement with the BCS gap equation and reveals the value of transition temperature as 36.78 K, 37.50 K, and 38.52 K for electron-phonon coupling constant (g_k) values 0.3, 0.7, and 1.1, respectively. This can be speculated from the obtained results that the T_c as well as superconducting gap (Δ) increases while approaching towards strong coupling regime from weak coupling regime. Also, the reduced gap ratio (2Δ(0) / k_BT_c ~ 6.5-7.0) is found in the limit (5-8) designated for HTS.