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CRC Press eBooks

Strongly coupled electrons and phonons

A. S. Alexandrov, Nevill Mott

Published Nov 24, 1994• 0 citations
Publisher

Abstract

In the adiabatic Migdal description of coupled electrons and phonons the instability appears at the bare coupling constant A ~ 1/2: the phonon frequency renormalised by the interaction u ~ u>\/l — 2A (Chapter 3). In a more general sense this is a boson vacuum instability driven by the strong interaction of fermionic and bosonic fields.

DOI
10.1201/9781482272673-9

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In the adiabatic Migdal description of coupled electrons and phonons the instability appears at the bare coupling constant A ~ 1/2: the phonon frequency renormalised by the interaction u ~ u>/l — 2A (Chapter 3). In a more general sense this is a boson vacuum instability driven by the strong interaction of fermionic and bosonic fields.
We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega} ratio, where vF{\mathit{v}}_{\mathit{F}}vF​ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when vF{\mathit{v}}_{\mathit{F}}vF​q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a CuO2{\mathrm{CuO}}_{2}CuO2​ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.
We study the Hubbard-Holstein model using slave-boson mean-field and a variational Lang-Firsov transformation. We identify weak and strong eee-ph coupling solutions, whose stability depends both on the bare eee-ph coupling and on the correlation strength. At mean field level the evolution from weak to strong electron-phonon coupling occurs via a first-order polaronic transition if the adiabatic parameter is below a critical value. In the strongly correlated regime and in the adiabatic limit, the region in which the weak-coupling solution is stable is sizeably enlarged with respect to the weakly correlated system and the Mott metal-insulator transition is found to be robust with respect to eee-ph interaction.