Far-infrared optical conductivity of YBCO single crystal thin films from transmission and reflection spectra

A new method to characterize the optical constants of thin films has been developed, and applied to YBa₂Cu₃O_7-x epitaxial single crystal thin films (T_c = 90 K) grown on MgO substrates to determine the far-infrared optical conductivity σ_ab(ω). In this method, both the transmittance and the reflectance spectra are measured and the results are substituted into a set of coupled equations which describe exactly the transmittance and reflectance of thin films on substrates, where the complex refractive indices n and k of the thin films are unknown parameters. The coupled equations are numerically solved by the Newton method, and the values of n and k are determined as functions of the wavenumber ω. We have determined σ_ab(ω) for YBa₂Cu₃O_7-x thin films in the range ω = 50-250 cm^-1 and T = 34-97 K. Analysis of the temperature dependence of σ_ab(ω) based on the two-fluid model suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.