Internal friction and ultrasonic attenuation related to carriers in high-Tc superconductors.

Abstract

For various samples of Bi-Sr-Ca-Cu-O (2:2:2:3 phase, 2:2:1:2 phase, and 2:2:2:3-2:2:1:2 mixed phases) and Tl-Ba-Ca-Cu-O (2:2:2:3 phase) with different ${\mathit{T}}_{\mathit{c}}$, the internal friction (${\mathit{Q}}^{\mathrm{\ensuremath{-}}1}$) in the kHz range reveals a plateau (${\mathit{Q}}_{\mathit{p}}^{\mathrm{\ensuremath{-}}1}$) above ${\mathit{T}}_{\mathit{c}}$ and drops drastically below ${\mathit{T}}_{\mathit{c}}$ with the turning point at ${\mathit{T}}_{\mathit{c}}$. This kind of anomaly has not been observed for nonsuperconducting samples. The results of ultrasonic attenuation (\ensuremath{\alpha}) in Tl-Ba-Ca-Cu-O (2:2:2:3) are similar to that of the internal friction mentioned above. Moreover, it is discovered that the ${\mathit{Q}}_{\mathit{p}}^{\mathrm{\ensuremath{-}}1}$ is nearly proportional to Hall carrier density (${\mathit{n}}_{\mathit{H}}$) for ${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$O and ${\mathrm{Gd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$O with various Pr content. These results indicate that the drastic drop of ${\mathit{Q}}^{\mathrm{\ensuremath{-}}1}$ and \ensuremath{\alpha} below ${\mathit{T}}_{\mathit{c}}$ is caused by superconducting condensation. The energy dissipation (${\mathit{Q}}_{\mathit{p}}^{\mathrm{\ensuremath{-}}1}$ and ${\mathit{a}}_{\mathit{p}}$) related to carriers can be explained reasonably by using a coupling model of carriers with local dynamic distortion. Furthermore, by taking into account the smearing of the superconducting gap structure caused by the recombination of quasiparticles and by modifying the BCS relative jump rate as S(E,E',\ensuremath{\Gamma})=Re{1-${\mathrm{\ensuremath{\Delta}}}^{2}$/[(E-i\ensuremath{\Gamma})(E'-i\ensuremath{\Gamma})]}, the calculated results of internal friction and ultrasonic attenuation below ${\mathit{T}}_{\mathit{c}}$ agree fairly well with the experimental data. The superconducting gap \ensuremath{\Delta} and the damping rate \ensuremath{\Gamma} for both Bi-Sr-Ca-Cu-O and Tl-Ba-Ca-Cu-O have also been obtained and are in accordance with those obtained by tunneling-spectrum, NMR methods, etc.