Precise measurements of the in-plane microwave surface impedance of
high-quality single crystals of Bi2212 and Tl2201 are used to probe the
relaxation time of nodal quasiparticles in the d-wave superconducting state
through a two-fluid analysis of the microwave conductivity. While this analysis
requires us to posit a form for the frequency-dependent quasiparticle
conductivity, we clearly demonstrate that the extraction of the relaxation rate
is quite insensitive to the assumed shape of the quasiparticle spectrum. The
robustness of the analysis is rooted in the oscillator-strength sum rule and
the fact that we simultaneously measure the real and imaginary parts of the
conductivity. In both Bi2212 and Tl2201 we infer a linear temperature
dependence of the transport relaxation rate 1/tau and a small but finite
zero-temperature intercept. The linear temperature dependence of 1/tau is in
accord with expectations for weak elastic scattering in an unconventional
superconductor with line nodes and a small residual density of states. The same
analysis reveals an onset of inelastic scattering at higher temperatures
similar to that seen in the YBCO superconductors. Finally we extrapolate the
two-fluid model over a range of frequencies up to five times the measurement
frequency, where the extrapolation predicts behaviour that is qualitatively
similar to terahertz conductivity data on Bi2212 thin films. While relaxation
rates in Bi2212 and Tl2201 are substantially higher than in YBCO there are
qualitative similarities between all three materials, and the differences can
likely be attributed to varying levels of static disorder. We therefore
conclude that a universal picture of quasiparticle scattering in the cuprates
is emerging.Comment: 10 pages, 9 figure