Two-fluid model analysis of the terahertz conductivity of YBaCuO samples: optimally doped, underdoped and overdoped cases

Abstract

The complex conductivity of underdoped and optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$ samples and overdoped similar compound Y$_{0.7}$Ca$_{0.3}$Ba$_2$Cu$_3$O$_{7-\delta}$ was measured using time-domain terahertz spectroscopy. In the normal state, the frequency dependence is described by the Drude model. Below the critical temperature $T_\mathrm{c}$, the two-fluid model was successfully employed to fit all the spectra, from 5 K up to $T_\mathrm{c}$. The temperature behaviour of fundamental parameters such as the scattering rate $1/\tau$, the superfluid (normal) fraction $f_\mathrm{s}$ ($f_\mathrm{n}$) and the conductivity $\sigma$ was investigated at given frequencies. For the optimally doped and the overdoped samples, even at 5 K, a fifth of the electrons do not condense to the superfluid fraction. We observed that a substantial fraction of electrons do not condense to the superfluid fraction even at 5 K for optimally doped and overdoped samples. The real part of the conductivity $\sigma_1(T)$ exhibits a peak at low frequencies. It can be observed for all three stoichiometries and its exact shape depends on the quality of the sample. A further analysis shows that this peak is a consequence of the competition between the scattering time $\tau(T)$ and the superfluid fraction $f_\mathrm{s}(T)$.