Properties of strong-coupled superconductors

Abstract

By use of Eliashberg equations the system of electrons and phonons with the Einstein spectrum ${\alpha }^2$(ω)F(ω)=(λΩ/2)δ(ω-Ω) is studied. The orbital and paramagnetic upper critical magnetic fields are obtained in the case of strong electron-phonon coupling λ (including λ≫1). For λ≫1, superconducting parameters at very low temperatures differ remarkably from those near $T_c$; the crossover takes place at a temperature corresponding to the phonon frequency Ω. For λ≳4, at temperatures below about Ω/3 the superconducting correlation length decreases, giving the positive curvature in the temperature dependence of the upper critical field. The coefficients of the Ginzburg-Landau functional are calculated. The absolute value of the specific-heat jump grows with λ while its relative value drops. For λ≳4, the resistivity above $T_c$ increases linearly with temperature.