Anomalous behavior of the complex conductivity of ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ observed with THz spectroscopy

We have measured the complex conductivity of ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ single-crystal thin films using coherent THz spectroscopy. We obtain directly the London penetration depth, the plasma frequency ${\mathrm{\omega }}_{\mathit{p}}$, and the quasiparticle scattering rate 1/τ. We find that 1/τ drops rapidly with temperature below ${\mathit{T}}_{\mathit{c}}$ in all the superconducting samples, implying that this is a signature of high-${\mathit{T}}_{\mathit{c}}$ superconductivity. ${\mathrm{\omega }}_{\mathit{p}}$ decreases with increasing x, indicating that Pr takes mobile carriers from the CuO planes. Both the THz and dc conductivity yield evidence for the opening of a spin gap above ${\mathit{T}}_{\mathit{c}}$.