Temperature dependence of far-infrared difference reflectivity of YBa2Cu

Abstract

Far-infrared difference reflectivity spectra (50--450 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) below, across and above the transition temperature on polycrystalline single-phase ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{y}}$ samples were measured. The data are compared with model fits using the explicit temperature dependence of the Mattis-Bardeen conductivity, an effective-medium approach and temperature-dependent phonon oscillator parameters and alternatively a plasma model. For the plasma model we alternatively use a generalized Drude-like expression with a frequency-dependent damping after Thomas et al. [Phys. Rev. B 36, 846 (1987)] or the original model with Orenstein et al. [Phys. Rev. B 36, 729 (1987)] and Sherwin, Richards, and Zettl [Phys. Rev. B 37, 1587 (1988)] with a Drude contribution plus a mid-infrared oscillator, but with constant carrier relaxation rates. The models explain the difference reflectivity data (precision 0.2%) with a fitting accuracy of 1--2 % (Mattis-Bardeen model) or 2--3 % (plasma model) over the full temperature range. In order to investigate their applicability, reflectivity, and conductivity data of a highly oriented ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{y}}$ sample, as recently published by Bonn et al. [Phys. Rev. Lett. 58, 2249 (1987)], were also fitted with both models. Because of the frequency dependence of the free-carrier damping rates, it was important to fulfill the Kramers-Kronig relations between the real and the imaginary part of the dynamic conductivity in the calculations. For both models the characteristic dependences of the conductivity on frequency and temperature are given. Whereas, naturally, the Mattis-Bardeen model yields a gaplike depression of the conductivity for frequencies below an assumed gap, the plasma model results in somewhat smoother dependences of Re(\ensuremath{\sigma}(\ensuremath{\omega})) and Im(\ensuremath{\sigma}(\ensuremath{\omega})) in the frequency region of interest.