| Issue |
Europhys. Lett.
Volume 56, Number 1, October 2001
|
|
|---|---|---|
| Page(s) | 92 - 98 | |
| Section | Condensed matter: electronic structure, electrical, magnetic, and opticalproperties | |
| DOI | https://doi.org/10.1209/epl/i2001-00492-x | |
| Published online | 01 December 2003 | |
Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
Department of Physics, Loughborough University -
Loughborough LE11 3TU, UK
Received:
16
February
2001
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
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