Superconductivity of Rb$_3$C$_{60}$: breakdown of the Migdal-Eliashberg theory

E. Cappelluti; C. Grimaldi; L. Pietronero; S. Strässler; G. A. Ummarino

doi:10.1007/PL00011123

paper

Superconductivity of Rb $_{3}$ C $_{60}$ : breakdown of the Migdal-Eliashberg theory

arXiv:cond-mat/0104457 · doi:10.1007/PL00011123

Abstract

In this paper, through an exhaustive analysis within the Migdal-Eliashberg theory, we show the incompatibility of experimental data of Rb $_{3}$ C $_{60}$ with the basic assumptions of the standard theory of superconductivity. For different models of the electron-phonon spectral function $α^{2} F (Ω)$ we solve numerically the Eliashberg equations to find which values of the electron-phonon coupling $λ$ , of the logarithmic phonon frequency $Ω_{l n}$ and of the Coulomb pseudopotential $μ^{*}$ reproduce the experimental data of Rb $_{3}$ C $_{60}$ . We find that the solutions are essentially independent of the particular shape of $α^{2} F (Ω)$ and that, to explain the experimental data of Rb $_{3}$ C $_{60}$ , one has to resort to extremely large couplings: $λ = 3.0 \pm 0.8$ . This results differs from the usual partial analyses reported up to now and we claim that this value exceeds the maximum allowed $λ$ compatible with the crystal lattice stability. Moreover, we show quantitatively that the obtained values of $λ$ and $Ω_{l n}$ strongly violate Migdal's theorem and consequently are incompatible with the Migdal-Eliashberg theory. One has therefore to consider the generalization of the theory of superconductivity in the nonadiabatic regime to account for the experimental properties of fullerides.

9 pages, 8 eps figure encloses, epjb style, to appear on Eur. Phys. J. B

Superconductivity of Rb3​C60​: breakdown of the Migdal-Eliashberg theory

Abstract

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Superconductivity of Rb $_{3}$ C $_{60}$ : breakdown of the Migdal-Eliashberg theory