On the limits of consistency of Eliashberg theory and the density of states of high-T _c superconductors

Abstract

We make a detailed study of the Eliashberg theory in the coupling region where some fundamental qualitative deviations from the conventional BCS-like behavior begin to appear. These deviations are identified as the onset of a cross-over from BCS superconductivity to Bose condensation. We point out that the beginning of this cross-over occurs when the gap δ _g becomes comparable to the boson energies Ω_ph. This condition traduces the physical constraint that the distance the paired electron covers during the absorption of the virtual boson, cannot be larger than the coherence length. The frontier region of couplings is of the order of λ ≈ 3, and high-T _c, materials are concerned. A clear qualitative indication of the occurrence of a crossover regime should be a dip structure above the gap in the density of states of excitations, and this is one of the most robust characteristics of the high-T _c, superconducting state. Comparing our results with tunneling and photoemission experiments we conclude that high-T _c materials (cuprates and fullerides) are indeed at the beginning of a cross-over from BCS superconductivity to Bose condensation, even though the fermionic nature still prevails. If the Uemura plot is relevant, then the dip should also be present in the other materials that are close to the cross-over regime like heavy Fermion and organic superconductors. In all these materials Ginzburg Landau equations are irrelevant.