Coupling to Phonons in the Migdal–Eliashberg Approach

Abstract

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 the- ory, which holds in low temperature superconductor sys- tems, the Migdal-Eliashberg approach implies serious lim- itations in the reproduction of experimental spectroscopies whose contributions are inter-band and not intra-band. Re- cent angle-resolved photoemission spectroscopy (ARPES) measurements on HTSC oxides whose contributions are intra-band show a kink in the quasiparticle spectrum at char- acteristic phonon frequencies in the normal and supercon- ducting state. In contrast with our theoretical discussion, we include our theoretical results for the renormalized energy Ek as a function of the bare band energy ek obtained from ARPES in a Pb sample and in a Bi2Sr2CaCu2O8+δ opti- mally doped sample (Bi2212). This is clear evidence that electron-phonon is strong and involved in pairing.