Temperature-dependent far-infrared reflectance of La-Sr-Cu-O and La-Ca-Cu-O: Bardeen-Cooper-Schrieffer electrodynamics but uncertain energy gap

The available far-infrared data for polycrystalline La-Sr-Cu-O and La-Ca-Cu-O show a reflectance edge with energy near 2.5$k_B$ $T_c$. This edge has been variously interpreted as the onset of absorption due to an energy gap, and as a low-frequency plasma edge caused by strong far-infrared resonances. Our measured temperature dependence of the reflectance edge closely fits the temperature dependence of the order parameter in a mean-field theory, and hence is consistent with the energy-gap hypothesis. In this paper, we construct a model dielectric function for ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ which is consistent with mean-field theory and the hypothesis of a plasma edge. We find that the temperature dependence of the plasma frequency in this model also closely fits the measured temperature dependence of the reflectance edge. Furthermore, both hypotheses accurately predict the experimentally observed temperature dependence of the absorption at frequencies much less than the reflectance edge. This observation has significant implications for the construction of fast low-loss superconducting devices. We conclude that the electrodynamics of the superconducting transition in ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ are well described by a Bardeen-Cooper-Schrieffer-like mean-field theory. However, given the identical predictions of the energy-gap and plasma-edge hypotheses, it is premature to deduce a precise value for the magnitude of the energy gap from the infrared data.