Far-infrared optical properties of superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$ films

The optical reflectance of thin superconducting ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{x}}$ (Bi 2:2:1:2) films has been studied in the frequency range 80–48 000 ${\mathrm{cm}}^{\mathrm{-}1}$ and the temperature range 5 K<T<300 K. Since the film thickness d is less than the optical skin depth δ, the reflectance from the film-substrate (${\mathrm{SrTiO}}_3$) interface must be considered in the interpretation of the experimental results. The dielectric function of the superconductor is calculated with use of the model of Leplae, which takes into account the effect of the quasiparticle lifetime. Structure in the reflectivity spectra is identified with Bi 2:2:1:2 phonons, ${\mathrm{SrTiO}}_3$ substrate phonons, and for T<${\mathit{T}}_{\mathit{c}}$, evidence for a superconducting gap is observed. The gap at T=5 K was found to be 2Δ=35±5 meV ≃6${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}}$, in good agreement with previous tunneling studies.