Phonon anomalies and range of superconducting energy gaps from infrared studies of YBa2Cu3O7−δ

Abstract

The infrared reflectivity of sintered ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, prepared under carefully controlled oxidation conditions, has been measured between 20 and 10 000 ${\mathrm{cm}}^{\mathrm{-}1}$ at temperatures between 10 and 300 K. In this paper we analyze in detail the temperature- and frequency-dependent far-infrared part of the spectrum. A Kramers-Kronig analysis allows us to compare the phonon part of the spectra with lattice-dynamical calculations. There is fairly good agreement concerning the assigned eigenfrequencies. The oscillator strengths of the experimentally observed phonons, however, are all stronger than those from a lattice-dynamics model which assumes ionic charges close to the formal ones. This is especially so for the lowest phonon found at 155 ${\mathrm{cm}}^{\mathrm{-}1}$ which shows a strength S=60±5 being about 15 times higher than theoretically expected. A possible origin of this effect is discussed qualitatively in terms of a Cu(1)-O(IV) charge shift during the vibration induced by the polarization field. The electronic background of the spectra has been analyzed by a Mattis-Bardeen type of dielectric response below $T_c$. The best fit yielded, for low T, a gap distribution in the range from about 160 to 370 ${\mathrm{cm}}^{\mathrm{-}1}$, corresponding to 2Δ(0)/$k_B$ $T_c$ values between 2.6 and 6.0.