Finite-temperature real-energy-axis solutions of the isotropic Eliashberg integral equations.

Abstract

A fast, efficient algorithm has been developed for calculating the finite-temperature real-energy-axis solutions of the Eliashberg integral equations for an arbitrary form of the electron-boson coupling function and Coulomb repulsion. Using this algorithm, the complex superconducting gap function {Delta}({omega},{ital T}), and the complex renormalization function {ital Z}({omega},{ital T}), have been obtained for a variety of forms of the electron-boson coupling spectrum. In addition, by calculating {Delta}({omega},{ital T}) at finite temperatures, the superconducting critical temperature {ital T}{sub {ital c}} has been obtained for a variety of model systems. These results compare well with the approximate analytic expression derived by Allen and Dynes for values of {lambda} less than 0.75. The solution of the Eliashberg equations has also been obtained for a model in which there are two well separated peaks in the electron-phonon coupling spectrum. This form of coupling spectrum is found to be particularly effective in raising the {ital T}{sub {ital c}} of the model system. Further, this model has been extended and the solution of the Eliashberg equations has been obtained with an electron-boson coupling spectrum consisting of both an electron-phonon component and a high-energy electronic electron-boson component. This form of the electron-boson coupling function may have special significancemore » in the field of high-temperature superconductivity. {copyright} {ital 1996 The American Physical Society.}« less