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 $f_{\mathrm{s}}(T)$.

8 pages, 6 figures + Supplemental material 2pages, 3 figures

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