Conductivity peak, relaxation dynamics, and superconducting gap of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ studied by terahertz and femtosecond optical spectroscopies

Recent measurements at microwave, terahertz (THz), and infrared frequencies have revealed a peak in ${\mathrm{\sigma }}_1$ below ${\mathit{T}}_{\mathit{c}}$. Based on our THz measurements, which were performed on high quality, single crystal films of YBCO (900 and 500 Å), we have found that ${\mathrm{\sigma }}_1$ features a peak which increases in amplitude and shifts to lower temperatures as frequency changes from 1.2 to 0.4 THz. Although the quasiparticle relaxation time extracted from these results using the two-fluid Drude model exhibits an enhancement below ${\mathit{T}}_{\mathit{c}}$, the analysis may not be adequate to account for the strong frequency dependence of the conductivity peak by the competition between the drop in scattering rate and the decreasing normal fluid density with temperature. On the contrary, we were able to account for the frequency dependent ${\mathrm{\sigma }}_1$ by fitting with Mattis-Bardeen theory (modified to include scattering) using a slower average rate of increase of the anisotropic gap than for the BCS case as temperature decreases below ${\mathit{T}}_{\mathit{c}}$. This is consistent with the higher normal fluid density (higher than Gorter-Casimir values) from the two-fluid model interpretation of our THz results. Thus, we have found evidence of BCS coherence factors in a high-${\mathit{T}}_{\mathit{c}}$ superconductor with a slower than BCS gap increase below ${\mathit{T}}_{\mathit{c}}$. We have discussed the role of coherence factors to account for the presence of the conductivity peak and the absence of the peak in NMR relaxation rate. Furthermore, we have presented a model for the quasiparticle relaxation time measured by the femtosecond pump-probe spectroscopy. This model allowed us to find a fit to the temperature-dependent energy gap function which is also consistent with the slower gap increase below ${\mathit{T}}_{\mathit{c}}$. In addition, recent theoretical developments based on an anisotropic s-wave gap [A. Sudbo/ et al., Phys. Rev. B 49, 12 245 (1994)] coincide with our conclusion about the slower gap change below ${\mathit{T}}_{\mathit{c}}$. © 1996 The American Physical Society.