The electron-phonon coupling coefficient for high-temperature superconductors

The expression for the electron-phonon coupling coefficient (g(k)) 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-delta cuprate superconductor has been used for the purpose of analysis and is found to be in agreement with the fact that g(k) decreases with the increase in temperature above 0 K. The distinct behavior obtained via dispersion for g(k) in different directions, [100] and [010], marked the anisotropy of electron-phonon coupling in HTSs. The derived expression for g(k) 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 T-c value for YBa2Cu3O7-delta, and the obtained reduced gap ratio [2 Delta (0)/k(B)T(c)] is found to be in the limit of the reduced gap ratio of HTSs.