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

Abstract A new method to characterize the optical constants of thin films has been developed, and applied to YBa 2 Cu 3 O 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 YBa 2 Cu 3 O 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.