ELIASHBERG EQUATION WRITTEN ON THE IMAGINARY AXIS FOR AN ISOTROPIC MEDIUM: SOLUTION ALGORITHM AND CALCULATION EXAMPLES

Abstract

At present, the task of searching for compounds with a high superconducting transition temperature ТС is a very relevant scientific direction. Usually, the calculation of ТС is performed by numerically solving the system of Eliashberg equations. This system is a system of integral equations, which, by discretizing the integrals included in it, is reduced to a system of transcendental non-linear equations, suitable for a numerical solution. In this paper, we present a set of programs for solving this system written in various forms on the imaginary axis for an isotropic medium. In addition, formulas for the Jacobian of this system are presented for the first time, the use of which in numerical calculations increases the speed and stability of calculations. As an example of the developed methods applications, the results of calculations of ТС and thermodynamic properties for the metallic hydrogen I41/amd phase under a pressure of 500 GPa are given. Also, the results of calculations of ТС for some metallic hydrides superconducting at high pressures, are given.