Nonadiabatic phenomenology in small Fermi energy superconductors

High-Tc and unconventional superconductivity appears in a number of different materials with different physical properties. A common characteristics shared by almost all these compounds is that they are 'bad metal' in the sense that their effective charge carrier density is quite small, leading to a small Fermi energy EF. In such a situation the dynamics of the electronic and lattice degrees of freedom becomes comparable (ωph∼EF) driving these systems towards a breakdown of the Born-Oppenheimer adiabatic principle (ωph≪EF) ruled by the comparison between the phonon frequency scale ωph and EF. The standard concept of Fermi liquid picture applied to the electron-phonon interaction needs thus to be deeply revised. We discuss the interesting implications of the onset of nonadiabatic effects on many properties of systems with small Fermi energy.