Determination of the optical properties of La _2-xBa _xCuO ₄ for several dopings, including the anomalous x=18 phase

The optical properties of single crystals of the high-temperature superconductor La _2-xBa _xCuO ₄ have been measured over a wide frequency and temperature range for light polarized in the a-b planes and along the c axis. Three different Ba concentrations have been examined, x=0.095 with a critical temperature T _c=32 K, x=0.125 where the superconductivity is dramatically weakened with T _c≃2.4 K, and x=0.145 with T _c≃24 K. The in-plane behavior of the optical conductivity for these materials at high temperature is described by a Drude-like response with a scattering rate that decreases with temperature. Below T _c in the x=0.095 and 0.145 materials there is a clear signature of the formation of a superconducting state in the optical properties allowing the superfluid density (ρ _s0) and the penetration depth to be determined. In the anomalous 1/8 phase, some spectral weight shifts from lower to higher frequency (≥300 cm ^-1) on cooling below the spin-ordering temperature T _so≃42 K, associated with the onset of spin-stripe order; we discuss alternative interpretations in terms of a conventional density-wave gap versus the response to pair-density-wave superconductivity. The two dopings for which a superconducting response is observed both fall on the universal scaling line ρ _s0/8≃4. 4σ _dcT _c, which is consistent with the observation of strong dissipation within the a-b planes. The optical properties for light polarized along the c axis reveal an insulating character dominated by lattice vibrations, superimposed on a weak electronic background. No Josephson plasma edge is observed in the low-frequency reflectance along the c axis for x=1/8; however, sharp plasma edges are observed for x=0.095 and 0.145 below T _c.