In-plane optical conductivity of La${}_{2-x}$Sr${}_x$CuO${}_4$: Reduced superconducting condensate and residual Drude-like response

Abstract

Temperature dependences of the optical spectra of La${}_{2-x}$Sr${}_x$CuO${}_4$ with $x$=0.12 and 0.15 were carefully examined for a polarization parallel to the CuO${}_2$-plane over a wide frequency range down to 8 cm${}^{-1}$. Selection of well-characterized crystals enabled us to measure purely in-plane polarized spectra without any additional peak. The weight of superconducting (SC) condensate estimated from the missing area in ${\sigma }_1(\omega$) well agrees with the estimate from the slope of ${\sigma }_2(\omega$) vs 1/$\omega$ plot, showing no evidence that the Ferrell-Glover-Tinkham sum-rule is violated in the optical spectrum. We demonstrate that the optically estimated SC condensate is much smaller than the value obtained from the $\mu$SR measurement of magnetic penetration depth. We also find an anomalous increase of conductivity in sub-millimeter region towards $\omega$=0 below $T_c$, which suggests the microscopic inhomogeneity in the superconducting state. Both observations are discussed in relation with the inhomogeneous electronic state that might be inherent to high-$T_c$ cuprates.

arXiv comment10 pages, 6 figures

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