Anomalous Behavior Of The Complex Conductivity Of Y_{1-x}Pr_xBa_2Cu_3O_7 Observed With THz Spectroscopy

We have measured the electrodynamic properties of Y_{1-x}Pr_xBa_2Cu_3O_7 single crystal thin films as a function of temperature using coherent THz-time-domain spectroscopy. We obtain directly the complex conductivity $\sigma=\sigma_1+i\sigma_2$, the London penetration depth $\lambda_L$, the plasma frequency $\omega_p$, and the quasiparticle scattering rate $1/\tau$. We find that $1/\tau$ drops exponentially rapidly with $T$ below the critical temperature in {\em all} the superconducting samples, implying that this behavior is a {\em signature} of high-$T_c$ superconductivity. The plasma frequency decreases with increasing Pr content, providing evidence that Pr depletes carriers, leaving the CuO planes {\em underdoped}. Both the conductivity in the THz region and the dc resistivity yield evidence for the opening of a spin gap {\em above} $T_c$.