Microwave determination of the quasiparticle scattering time inYBa2Cu3O6.95

Abstract

We report microwave surface resistance (${\mathit{R}}_{\mathit{s}}$) measurements on two very-high-quality ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.95}$ crystals which exhibit extremely low residual loss at 1.2 K (2-6 \ensuremath{\mu}\ensuremath{\Omega} at 2 GHz), a broad, reproducible peak at around 38 K, and a rapid increase in loss, by 4 orders of magnitude, between 80 and 93 K. These data provide one ingredient in the determination of the temperature dependence of the real part of the microwave conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(T), and of the quasiparticle scattering time. The other necessary ingredient is an accurate knowledge of the magnitude and temperature dependence of the London penetration depth, \ensuremath{\lambda}(T). This is derived from published data, from microwave data of Anlage, Langley, and co-workers and from, high-quality \ensuremath{\mu}SR data. We infer, from a careful analysis of all available data, that ${\ensuremath{\lambda}}^{2}$(0)/${\ensuremath{\lambda}}^{2}$(T) is well approximated by the simple function 1-${\mathit{t}}^{2}$, where t=T/${\mathit{T}}_{\mathit{c}}$, and that the low-temperature data are incompatible with the existence of an s-wave, BCS-like gap. Combining the ${\mathit{R}}_{\mathit{s}}$ and \ensuremath{\lambda}(T) data, we find that ${\mathrm{\ensuremath{\sigma}}}_{1}$(T), has a broad peak around 32 K with a value about 20 times that at ${\mathit{T}}_{\mathit{c}}$. Using a generalized two-fluid model, we extract the temperature dependence of the quasiparticle scattering rate which follows an exponential law, exp(T/${\mathit{T}}_{0}$), where ${\mathit{T}}_{0}$\ensuremath{\approxeq}12 K, for T between 15 and 84 K. Such a temperature dependence has previously been observed in measurements of the nuclear spin-lattice relaxation rate. Both the uncertainties in our analysis and the implications for the mechanism of high-temperature superconductivity are discussed.