Electron-phonon renormalization in small Fermi energy systems

The puzzling features of recent photoemission data in cuprates have been the object of several analyses in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basic assumptions of the conventional analysis are expected to fail in small Fermi energy systems, when, as in the cuprates, the Fermi energy E-F is comparable with the boson energy scale. We discuss in detail the features appearing in the self-energy of small Fermi energy systems and the possible implications for the angle-resolved photoemission spectroscopy data in cuprates.