Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
Department of Physics, Loughborough University -
Loughborough LE11 3TU, UK
Accepted: 10 July 2001
In view of some recent works on the role of vertex corrections in the electron-phonon system, we readdress the important question of the validity of the Migdal-Eliashberg theory. Based on the solution of the Holstein model and strong-coupling expansion, we argue that the standard Feynman-Dyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electron-phonon coupling is strong () at any ratio of the phonon, ω and Fermi, energies. In the extreme adiabatic limit () of the Holstein model electrons collapse into self-trapped small polarons or bipolarons due to spontaneous translational-symmetry breaking at . With the increasing phonon frequency the region of the applicability of the theory shrinks to lower values of .
PACS: 74.20.-z – Theories and models of superconducting state / 74.20.Mn – Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) / 71.38.-k – Polarons and electron-phonon interactions
© EDP Sciences, 2001