Internal friction and ultrasonic attenuation related to carriers in high T _c superconductors

For both BiSrCaCuO and TlBaCaCuO samples, internal frictions (Q-1) in the kHz range reveal a plateau (Q-1p) above Tc and a rapid drop below Tc with the turning points located just at Tc for various samples with different Tc. This anomaly cannot be observed in non-superconducting samples. The ultrasonic attenuation (α) in TlBaCaCuO displays similar results to the internal friction. Moreover, it is discovered that the Q-1p is nearly proportional to the carrier density for Y(Pr)BaCuO and Gd(Pr)BaCuO with different Pr contents. These results show that the drop of Q-1 and α below Tc is closely related to superconducting condensation. The Q-1p and αp can be explained using coupling-model of carriers with local dynamic distortion because high Tc superconductors are strong-correlation systems. Furthermore, by taking account of the smearing of superconducting gap structure resulting from the recombination of quasi-particles and by modifying the BCS relative jump rate as S(E, E', Γ) = Re{1-Δ2/[(E-iΓ)(E'-iΓ)]}, the calculated results of internal friction and ultrasonic attenuation below Tc are in good agreement with the experimental data. The superconducting gap Δ and the damping rate Γ for both BiSrCaCuO and TlBaCaCuO have also been obtained, they are in accordance with those got by tunneling spectrum and NMR methods, etc.