Eliashberg analysis of the optical conductivity in superconducting Pr${}_2$CuO${}_x$ ($x\simeq 4$)

Superconducting Pr${}_2$CuO${}_x$, $x\simeq 4$ films with $T^{\mathrm{\prime }}$ structure and a $T_c$ of 27 K have been investigated by millimeter-wave transmission and broadband (infrared-to-ultraviolet) reflectivity measurements in the normal and superconducting state. The results obtained by both experimental methods show a consistent picture of the superconducting condensate formation below $T_c$. An Eliashberg analysis of the data proves $d$-wave superconductivity and unitary-limit impurity scattering of the charge carriers below $T_c$. The derived electron-exchange boson interaction spectral function $I^2\chi (\omega )$ shows only marginal changes at the superconducting transition with the mass enhancement factor $\lambda$, the first inverse moment of $I^2\chi (\omega )$, being equal to 4.16 at 30 K and to 4.25 at 4 K.