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- Seitenbereich
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0431 - 0450
- Schlagwort(e)
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<KWD>Superconductivity
Eliashberg equations
High-<i>T<sub>c</sub></i> cuprates
Organic superconductors
- Zusammenfsg.
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We solve the Eliashberg equations for the case of an explicit <I>k</I> dependence of the interactions, and of the resulting self-energies σ<sub>1</sub>(<I>k</I>,ω), σ<sub>2</sub>(<I>k</I>,ω). We consider a strong energy-dependence of the electron-electron scattering-rate τ<sub>ee</sub><sup>-1</sup>, which is associated with a strong energy-dependence of the electron-phonon matrix element <I>g</I>(<I>k,k</I>´). We characterize this energy-dependence by a cutoff ζ<sub>1</sub>, which is of the order of the phonon frequency ω<sub>ph</sub>. We find that we can account for a large number of unexpected features of the superconductivity of the cuprates by the BCS electron-phonon theory, if we consider very large values of the McMillan coupling constant λ<sub>ph</sub>, and small values of the cutoff ζ<sub>1</sub>. Specifically, the Coulomb interaction is found not to depress <I>T<sub>c</sub></I>; the isotope effect is strongly reduced when ζ<sub>1</sub> < ω<sub>ph</sub>. We find solutions in which the gap function Δ(<I>k</I>, ω) has extended <I>s</I>-wave symmetry but is very anisotropic. These large anisotropies are in good agreement with various experiments. We suggest that the underlying cause of the strong energy-dependence is a very small electronic screening parameter at the Fermi surface; the electron-phonon matrix element <I>g</I> is abnormally large, and this accounts for the high transition temperatures of the cuprates. An order of magnitude estimate suggests that the electron-phonon mechanism can account for transition temperatures up to about 200 K. We thus propose a very-strong-coupling theory, in which the renormalization functions, in particular the energy-renormalization <I>X</I>, depend very strongly on the superconducting gap Δ, and thus display a very strong temperature-dependence between <I>T<sub>c</sub></I> and <I>T</I> = 0. An experimental manifestation of the very strong coupling with a small cutoff is a zero bias anomaly sometimes observed in tunneling experiments.
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