16. We quantify the possible effects of the breakdown of Migdal's theorem on the electron-phonon coupling constant, on the critical temperature and on the superconducting gap by examining different kinds of superconducting materials (figure 1, figure 2) either with low and high critical temperature. We use the theoretical approach developed by Grimaldi, Pietronero and Strassler [PRB 52, 10516 & 10530 (1995)] on experimental data taken both from literature. The results show that a large violation of the Migdal's theorem yields to a large increase of the observed electron-phonon coupling constant and, in a first approximation and by direct solution of the Eliashberg equations, to large but different increases of T_c and gap. The same theory gives no modifications when applied to low-T_c conventional superconductors. In Bi₂Sr₂CaCu₂O_8+x, the renormalized values of the electron-phonon coupling constant and of the ratio 2D/k_B T_c (1.85 and 4.98, respectively) are compatible with a strong-coupling electron-phonon origin of superconductivity.

E. Cappelluti, C. Grimaldi, L. Pietronero, S. Strassler, G.A. Ummarino
"Superconductivity of Rb₃C₆0: breakdown of the Migdal-Eliashberg theory ", European Physical Journal B, 21, 383-391, (2001).

G.A. Ummarino, R.S. Gonnelli
"Some consequences of the breakdown of Migdal’s Theorem in high-T_c superconductors ", Physica C, 317-318, 524-527, (1999).

G.A. Ummarino, R.S. Gonnelli
"The effects of the breakdown of Migdal’s Theorem in various superconductors ", International Journal of Modern Physics B, vol. 13, n. 9&10, 1215-1220, (1999).

G.A. Ummarino, R.S. Gonnelli
"Breakdown of Migdal’s Theorem and intensity of electron-phonon coupling in high-T_c superconductors", Physical Review B - Rapid Comm., 56, R14279-R14283, (1997).