The Violation of the BCS Theory and the Extensions required to include the Effects of a nearby Phase Transition

Abstract

While numerous experimental results support the conventional BCS electron-phonon mechanism, quite a number of specific data like the specific heat jump and the critical magnetic fields lie up to a factor of two above the predictions of the strong coupling BCS/Eliashberg theory using all of the experimental phonons. In particular the observed dependence of the electron-phonon matrix element on the vibrational amplitude for strong coupling superconductors violates the BCS theory. It is proposed to account for high temperature superconductivity in terms of a largely conventional BCS /Eliashberg-theory, extended to include additionally the effects of a nearby structural phase transition (SPT). Experimental data show that the SPT at the temperature Tp causes a resonance like enhancement of the phonon population numbers with energies near kBTp. In many respects, these additional vibrations of the SPT act like an additional broad phonon with an integrated intensity comparable to that of the narrow normal mode phonons. In addition in the HTS systems, there are several broad “phonons” associated with spatial gaps in the structure. These are the explanation for the “electronic” states in the gap. Hence in the calculation of the superconducting and thermodynamic quantities using the Eliashberg theory all of these have to be taken into account. The total phonon spectrum F(e) includes the narrow regular normal mode phonons and these broad gap modes as evidenced by diffuse X-ray scattering. These additional phonons provide the factor of more than two in the measure of strength of the electron-phonon interaction A =∫α2F(e)de required to account for the Tc of the HTS and give the low value of λ ab = 1.4. The physical reasons for the choice of this ansatz are discussed. It corresponds to the Frohlich /Weisskopf picture, extended by including the effect of a nearby SPT. The specific heat of the superconducting phase transition sits on the tail of that of the SPT. When this is allowed for, one obtains the expected exponential shape for s-wave superconductivity with a fitted scalar gap twice the value as calculated from Tc. The specific heat jump △Cp is due not only to the usual electronic part, but also to an ionic part of comparable magnitude. Hence the critical fields and the gap are also twice the BCS value as confirmed by data. Results are presented for the calculation of Tc and the isotope effect as function of the Sr-fraction for La-214 and as function of the oxygen content for Y-123 and are in good agreement with the data. The enhancement through the SPT leads to the coupling of the superconducting and the structural order parameters. The qualitative agreement of numerous further experimental data with the present ansatz confirms it.