The superconductivity-induced self-energy of phonons has been calculated in the lowest-order conserving approximation using conventional strong-coupling theory and also including scattering at nonmagnetic impurities. Results for the dependence of the shift and the width of phonons on temperature and scattering rates are presented and their sensitivity on the strength of the electron-phonon coupling and on impurities is pointed out. The theory is applied to optical data in YBa2Cu3O7 using the experimental one-phonon density, the value ofT

 c
 and [*=0.25 as inputs. Neglecting anisotropies and the momentum dependence of the electron-phonon coupling the resulting strong-coupling model with λ≈2.9 yields results which are in good agreement with the data, in particular, if impurity scattering is taken into account.

Superconductivity-induced phonon self-energy effects in high-T c superconductors

Raman and IR-measurements on the high- T c material series La 2 CuO 4 and YBa 2 Cu 3 O 7 are reviewed. This summary focuses on lattice vibrations in these superconducting systems, on impurity phases, the influence of oxygen stoichiometry and element substitution. The determination of the superconducting gap, the phonon renormalization in the superconducting state, and the isotope effect with its implications on the theory of superconductivity in these materials are discussed. In addition, the measured lattice vibrations are compared with the results of lattice dynamics calculations.

Lattice vibrations in high-Tc superconductors: Optical spectroscopy and lattice dynamics☆

The infrared reflectivity of sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, prepared under carefully controlled oxidation conditions, has been measured between 20 and 10 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ 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 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ which shows a strength S=60\ifmmode\pm\else\textpm\fi{}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 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, corresponding to 2\ensuremath{\Delta}(0)/${k}_{B}$${T}_{c}$ values between 2.6 and 6.0.

Phonon anomalies and range of superconducting energy gaps from infrared studies of YBa2Cu3O7- delta.

We report a Raman scattering investigation of superconducting gap anisotropy in single-crystal $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. Gap anisotropy is investigated by studying the peak in the low-temperature Raman continuum in various symmetries. Roughly a 35% difference in the energy of this peak is observed between different symmetries, suggesting the presence of substantial gap anisotropy. Anisotropy is further evidenced by the damping behavior of the 340-${\mathrm{cm}}^{\ensuremath{-}1}$ Raman-active phonon below ${T}_{c}$, which displays increased attenuation due to phonon-induced pair breaking. The temperature dependence of this attenuation is consistent with a $T=0$ pair-breaking peak which is much larger than the 340-${\mathrm{cm}}^{\ensuremath{-}1}$ phonon in certain regions of the Fermi surface.

Gap anisotropy and phonon self-energy effects in single-crystal YBa2Cu3O7- delta.

Raman scattering experiments have been performed on single-crystal samples of Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ in order to investigate superconducting gap excitations. The electronic contribution to the total scattering intensity can be fitted well by a theoretical model of light scattering from quasiparticle pairs. Depending on the measuring symmetry, mean gap energies are found ranging from 3.0 to $5.5 {k}_{B}{T}_{c}$.

Light-scattering study of the superconducting energy gap in Y Ba 2 Cu 3 O 7 single crystals

We present a far-infrared study of ceramic superconductors of the MBa/sub 2/Cu/sub 3/O/sub 7/ family with M = Dy, Sm/sub 0.5/Ho/sub 0.5/, and Sm/sub 0.5/Y/sub 0.5/. Emphasis is placed on the determination of the position of the superconducting energy gap E/sub g/ and its temperature dependence. We find that for all compositions studied E/sub g//k/sub E/T/sub c/approx. =3.2 +- 0.3. We also find indications of the temperature dependence of the gap and discuss the influence of the phonon features on the quantitative determination of the gap position.

Superconducting energy gap in MBa

High Tc superconductors MBa2Cu3O7−x with M = Mixed Rare earths and Y: Low frequency phonon peak engineering

We present a far-infrared (FIR) study of superconductors of the MBa 2 Cu 3 O 7−x family with M=Y,Dy,Sm 0, 5 H 0, 5 Sm 0, 5 Tm,Er,Nd,Ho. Emphasis is placed on the superconducting energy gap E g , its temperature dependence K and the temperature dependence of optical phonons. We find that for all compositions studied E g /kT c 3.5±0.3 and we also find the indications of the temperature dependence of the gap. A phonon softening with decreasing temperature for T T c is observed for the modes attributed to bending vibrations of the Cu II -O 2 and Cu III -O 3 bonds.

Superconducting energy gap and phonon spectra in MBa2Cu3O7−x type materials

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Superconducting energy gap in MBa

High Tc superconductors MBa2Cu3O7−x with M = Mixed Rare earths and Y: Low frequency phonon peak engineering

Superconducting energy gap and phonon spectra in MBa2Cu3O7−x type materials