In-plane optical response in underdoped YBCO

The recent STM experiments demonstrated that the electronic state in CuO$_{2}$ plane is inhomogeneous [1], which becomes conspicuous in the underdoped regime. In such an inhomogeneous state, it is not obvious whether a superfluid density is correctly estimated by a conventional way. We investigated the in-plane optical response for underdoped YBCO crystal to discuss the relation between inhomogeneity and superfluid density in the pseudo-gapped state. The a-axis optical spectrum shows a larger residual conductivity than that for the optimum doping. The superfluid density estimated from our optical spectrum at the lowest temperature is substantially smaller than that determined by $\mu $SR. We discuss this strongly suppressed superfluid density and the large residual conductivity in terms of the inhomogeneity in real- and k-space. This work was supported by the New Energy and Industrial Technology Development Organization(NEDO) through ISTEC as the Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications. [1]K.M.Lang et al., Nature 415, 412 (2002). *present address: Dept. of Physics, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan