The investigation of Eliashberg equations for superconductors with strong electron-phonon interaction

Abstract

The superconductivity state in systems with strong electron-phonon interacting is studied. Eliashberg equation is transformed in the form, in which nonresonant terms which has energetical dependence similar to that in BSC theory and resonance terms (caused by specific of retarded electron-phonon interaction) are extracted. It is shown, that resonance terms increase with the constant of electron-phonon interaction λ and for large λ ⪢ 1 they mostly determine behavior both of T c and of the gap Δ 0. This leads to the behavior of the gap as Δ 0 ≅ λ . Using spectral density of electron-phonon interaction α 2(ω) F(ω) which corresponds HTSC compounds we have studied the behavior of density of states of electrons N s (ω) and have shown the essential difference from those in BCS theory mainly for temperatures near T c . Corresponding behavior N s (ω) leads to the differences in behavior of kinetic and thermodynamic characteristics of superconductors from BCS theory near T c , that was demonstrated for the number of superconducting electrons and the London-limit penetration depth.