Coupling to Phonons in the Migdal–Eliashberg Approach

The relevance of the strong correlations in the high critical temperature superconductors (HTSC) is well experimentally documented. However, if the properties of the normal and superconducting state in HTSC oxides are interpreted in terms of the standard Eliashberg theory, which holds in low temperature superconductor systems, the Migdal–Eliashberg approach implies serious limitations in the reproduction of experimental spectroscopies whose contributions are inter-band and not intra-band. Recent angle-resolved photoemission spectroscopy (ARPES) measurements on HTSC oxides whose contributions are intra-band show a kink in the quasiparticle spectrum at characteristic phonon frequencies in the normal and superconducting state. In contrast with our theoretical discussion, we include our theoretical results for the renormalized energy E k as a function of the bare band energy ε k obtained from ARPES in a Pb sample and in a Bi 2 Sr 2 CaCu 2 O 8+ δ optimally doped sample (Bi2212). This is clear evidence that electron-phonon is strong and involved in pairing.