Electron-phonon driven unconventional superconductivity: The role of small Fermi energies and of nonadiabatic processes

The very concept of high-T-c superconductivity has originated from the discovery of superconductivity in copper oxides by Bednorz and Muller in 1986. Soon after their discovery, cuprates were recognized as undoubtedly complex and radically unconventional superconducting materials, and research to understand the origin of superconducting phase has since then mainly focused on the strong-correlation aspects of these compounds, whereas the role of the electron-phonon coupling has been mostly ignored by much of the scientific community. Nowadays, however, thanks also to the steady later research of K.A. Muller, the presence of a relevant role of the electron-phonon coupling, in a unconventional scenario, has been assessed. Due to the small carrier concentration, and hence to the small Fermi energies, one of the concepts that needs to be revised in these compounds is the assumption of adiabaticity. In this contribution we summarize the main directions followed in this field for defining a microscopic theory of superconductivity in the nonadiabatic regime. The differences of such analysis with respect to a polaronic scenario are also discussed, as are some complementary paths of investigation of the complex many-body electron-phonon problem in different physical regimes.