Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: In-plane optical conductivity of La$_{2-x}$Sr$_x$CuO$_4$: Reduced
  superconducting condensate and residual Drude-like response   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.

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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys