---
abstract: 'The complex transmission of $\rm Y_{1-x}Pr_xBa_2Cu_3O_7$ single crystal thin films has been measured in the range 0.2-1.0 THz using time domain spectroscopy. The complex conductivity is calculated without using a Kramers-Kronig analysis. All of the superconducting samples show a peak in $\sigma_1(T)$ below $T_c$. The underdoped samples show a deviation from $1/(\alpha+\beta T)$ behavior above $T_c$ that may be linked with the onset of a spin gap.'
address: 'Max-Planck-Institut für Festkörperforschung, Postfach 800665, 70506 Stuttgart, Germany'
author:
- 'J.O. White[^1], R. Buhleier, S.D. Brorson[^2], I.E. Trofimov[^3], H.-U. Habermeier, and J. Kuhl'
title: 'Complex conductivity of $\rm Y_{1-x}Pr_xBa_2Cu_3O_7$ thin films measured by coherent terahertz spectroscopy'
---

\#1 \#2[$\rm Y_{#1}Pr_{#2}BCO$]{} \#1 \#2[$\rm Y_{#1}Pr_{#2}Ba_2Cu_3O_7$]{}

INTRODUCTION
============

The spectroscopic data on the high-$T_c$ superconducting compound $\rm Y_1Ba_2Cu_3O_7$ measured in the far infrared (FIR) as well as the GHz-region has revealed many interesting features. The new technique of THz-time-domain spectroscopy bridges the gap between the two regimes. Here we report results of a THz investigation into the xYPrBCO) system. We investigated five YPrBCO samples having Pr composition $x$ = 0.0, 0.2, 0.3, 0.4, and 1.0. The films are grown to a thickness of 150 nm by pulsed laser deposition [@habermeier91] onto NdGaO$_3$ substrates.

Our spectroscopic technique involves a time-domain measurement of the electric field of a microwave pulse transmitted through the sample [@brorson94]. A Fourier transform yields the complex transmission spectrum. To calculate the conductivity, we make use of a multiple reflection formula for the field transmitted through the YBCO layer.

RESULTS
=======

The conductivity spectra at 50 K are shown in Fig. \[sigma\_nu\]. The addition of Pr to YBCO should have at least two interrelated effects: a) The suppression of $T_c$ changes the partitioning between normal and superconducting carriers. b) The total number of carriers $N$ (or their mobility) may be reduced.

Both factors a) and b) cause $\sigma_2$ to decrease with \[Pr\]. Only normal carriers contribute to $\sigma_1$ for $\omega \neq 0$, but now factors a) and b) compete. At 50 K, $\sigma_1$ decreases with \[Pr\], therefore the effect of a reduction in $N$ dominates the effect of the shift in $T_c$. For 30% and 40% Pr, we observe a frequency dependent $\sigma_1$ and can directly measure $\tau(T)$, the quasi-particle scattering time. Pure PrBCO is a dielectric at 50 K, as seen by a conductivity proportional to frequency.

Examining $\sigma_2(T)$ at a fixed frequency (Fig. \[sigma\_T\]a), we see that it is close to zero at high temperature, but rises sharply at the onset of superconductivity, thus providing an ac measurement of $T_c$ (Table 1).

In all of the superconducting alloys, $\sigma_1$ displays a peak below $T_c$ which has been seen previously only in pure YBCO. It has been attributed to a sharp rise in the scattering time dominating the effect of a decrease in the number of normal carriers [@nuss91].

The normal state behavior of our samples is particularly interesting because other [*underdoped*]{} materials such as oxygen deprived (123)YBCO undergo a phase transition associated with the opening of a spin gap at $T_D>T_c$ [@ito93]. If the normal carriers couple strongly to spin fluctuations, the opening of a spin gap should be accompanied by an [*increase*]{} in the scattering time $\tau$, giving rise to an [*enhancement*]{} in $\sigma_1$ below $T_D$ for $\omega<1/\tau$.

For pure (optimally doped) YBCO, at 480 GHz, $\sigma_1$ shows only a single transition at $T_c$. For the (underdoped) alloys, $\sigma_1$ has two transitions, one at $T_c$, the other at a higher temperature which increases with \[Pr\]. To accentuate the two transitions, Fig. \[sigma\_T\]b is shaded in the region bounded by $T_c$, the experimental curve, and a dashed line representing $1 / (\alpha+\beta T)$ behavior. The higher transition temperature seen at 480 GHz matches that of a transition also observed in the dc resistivity.

We evaluate the penetration depth $\lambda_L$ and the plasma frequency $\omega_p$ by fitting the data to a two fluid model of the form: $$\sigma(\omega) = {\epsilon_0 \omega_p^2 \tau
\over {1-i\omega\tau}}x_n +
{1 \over {\mu_0\lambda_L^2}}\left(- \pi\delta(\omega) + {i \over \omega}
\right) x_s,
\label{2fluid}$$ where $x_n$ and $x_s$ are the fractions of normal and superconducting carriers. The results are shown in Table 1. The decrease in $\omega_p$ with \[Pr\] supports the theory that Pr suppresses superconductivity by reducing the population of mobile holes in the $\rm CuO_2$ planes.

   $x$   $d$ (nm)   $\lambda_L$ (nm)   $\omega_p$ (cm$^{-1}$)   $T_c^{\rm ac}$ (K)
  ----- ---------- ------------------ ------------------------ --------------------
   0.0     155            170                   9500                    92
   0.2     134            350                   4600                    72
   0.3     170            380                   4200                    59
   0.4     170            590                   2700                    41

[9]{}

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S. D. Brorson [*et al.*]{}, Phys. Rev. B [**49**]{}, 6185 (1994).

M. C. Nuss [*et al.*]{}, Phys. Rev. Lett [**66**]{}, 3305 (1991).

T. Ito, K. Takenaka, and S. Uchida, Phys. Rev. Lett. [**70**]{}, 3995 (1993).

[^1]: on leave from: Hughes Research Laboratories, Malibu.

[^2]: present addr.: Teledanmark Laboratories, Copenhagen.

[^3]: present address: Rutgers University, Piscataway, NJ.
