Nonadiabatic theory of the superconducting state

Abstract

and INFM, Unità Roma1Fermi energies in fullerene compounds and cuprates are extremely small as consequence of the small number of charge carriers and are comparable to the phonon frequency scale. In this situation the conventional Migdal-Eliashberg theory does not hold anymore and nonadiabatic effects need to be taken into account. In previous studies, a generalization of Eliashberg theory in the nonadiabatic regime has been proposed to calculate normal state properties and the onset temperature Tc of the superconductive phase. Here we extend the nonadiabatic theory below Tc where the opening of the superconducting order parameter affects the nonadiabatic correction. The superconducting gap ∆ is calculated in a self-consistent way. We find that large values of the ratio 2∆/Tc are obtained in the nonadiabatic theory by smaller electron-phonon coupling λ than in Migdal-Eliashberg theory. This agrees with the picture that strong-coupling phenomenology can be achieved in nonadiabatic theory by "reasonable" values of λ. We apply our analysis to the case of the fullerene compounds.

A review of electron–phonon coupling seen in the high‐Tc superconductors by angle‐resolved photoemission studies (ARPES)

“…Non-adiabatic effect beyond the Migdal approximation have been considered and are under continuing study [50].…”

Nonadiabatic breakdown and pairing in high-Tc compounds

“…The Nambu formalism permits to generalize the nonadiabatic theory of superconductivity also below the critical temperature T c to evaluate zero temperature quantities as for instance the superconducting gap D. The formal derivation is not difficult but quite tedious and we refer to Ref. 64 for technical details. An important point is that the vertex and cross functions, as well the corresponding nondiagonal quantities in the Nambu space, need to be evaluated in the presence of the superconducting gap which partially reduces the nonanaliticity of these function at the (q = 0, w = 0) point.…”

“…13 which shows that the net result of the opening of the superconducting gap is to reduce the positive region of the vertex function and to increase the negative one. A direct consequence of this effect is that the effective superconducting pairing in the superconducting state at T = 0 is smaller than the one at T T c = , so that the ratio 2D/T c , for a given l, is smaller in the nonadiabatic framework than in ME theory [64].…”

Low-Temperature Thermodynamic Properties of Superconducting Antiperovskite CdCNi $$_3$$ 3

“…The precise prediction of superconducting properties such as the transition temperature, superconducting energy gap or specific heat is one of the most important challenges in condensed matter physics [37][38][39][40][41][42]. In conventional superconductors below the critical temperature electron pairing results from interplay between the electron-electron repulsive Coulomb effect and the attractive electron-phonon interaction [43].…”