Eliashberg equations of electrons on a square lattice: Interplay of strong electron-phonon interactions and electron correlations

Journal Article · Thu Jan 01 04:00:00 EST 1998 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.57.590· OSTI ID:565898

Mierzejewski, M; Zielinski, J ^[1]; Entel, P ^[2]

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1. Institute of Physics, University of Silesia, 40-007 Katowice (Poland)
2. Theoretische Physik, Gerhard-Mercator-Universitaet Duisburg, 47048 Duisburg (Germany)

We discuss vertex corrections to the Eliashberg equations of correlated electrons due to strong electron-phonon interactions. Local electron correlations have been taken into account in the mean-field approximation for slave-boson fields in the U{r_arrow}{infinity} limit of the two-dimensional Hubbard model. The modification of the wave-function renormalization factor originating from vertex corrections has been evaluated in a self-consistent way. We have considered both ionic and covalent parts of the electron-phonon interaction as possible pairing mechanisms. For the ionic contribution at low doping (strong-coupling limit), inclusion of vertex corrections leads to a decrease of the superconducting transition temperature T{sub c} for d-wave symmetry. This decrease agrees with the experimentally observed dependence of T{sub c} on the concentration of holes and originates from the enhancement of the density of states near the van Hove singularities due to correlations. Another important effect originating from inclusion of vertex corrections is a pronounced reduction of the isotope shift exponent {alpha} at optimal doping. This supports the view that experimentally observed small values of {alpha} still allow for phonon-induced superconductivity in strongly correlated systems. We discuss the controversial question with respect to the sign with which the vertex corrections contribute to the pairing kernels of the Eliashberg equations of strongly correlated electron-phonon systems. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 565898
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 1 Vol. 57; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ELECTRON-PHONON COUPLING
ENERGY-LEVEL DENSITY
FERMI LEVEL
GORKOV-ELIASHBERG THEORY
HIGH-TC SUPERCONDUCTORS
HUBBARD MODEL
SUPERCONDUCTIVITY
TRANSITION TEMPERATURE
VORTICES