The electron–phonon coupling coefficient for high-temperature superconductors

The expression for the electron–phonon coupling coefficient (gk) is obtained by solving a six order polynomial equation obtained via the quantum dynamical many-body theory of the electron and phonon Green’s function for high-temperature superconductors (HTSs). The developed equation depends on the temperature; electron, phonon, and pairon frequencies; and distribution functions. The YBa2Cu3O7−δ cuprate superconductor has been used for the purpose of analysis and is found to be in agreement with the fact that gk decreases with the increase in temperature above 0 K. The distinct behavior obtained via dispersion for gk in different directions, [100] and [010], marked the anisotropy of electron–phonon coupling in HTSs. The derived expression for gk is further used for the evaluation of the superconducting gap via the Bardeen–Cooper–Schrieffer and the McMillan gap equation and both superconducting gap equations approach the Tc value for YBa2Cu3O7−δ, and the obtained reduced gap ratio [2Δ(0)/kBTc] is found to be in the limit of the reduced gap ratio of HTSs.