Frequency-dependent relaxation rate in superconducting YBa 2 Cu 3 O 6 + δ

The submillimeter-wave 3 cm − 1 <ν < 40 cm − 1 complex conductivity of the reduced YBa 2 Cu 3 O 6+ δ film ( T C =56.5 K) was investigated for temperatures 4 K <T < 300 K and compared to the properties of the same film in the optimally doped state. The frequency dependence of the effective quasiparticle scattering rate 1 /τ ∗ ( ν ) was extracted from the spectra. 1 /τ ∗ is shown to be frequency independent at low frequencies and high temperatures. A gradual change to 1 /τ ∗ ∝ ν 1 . 75 ± 0 . 3 law is observed as temperature decreases. In order to explain the observed temperature dependence of the low frequency spectral weight above T C , the quasiparticle effective mass is supposed to be temperature dependent for T>T C .