Electron scattering rate in epitaxial ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ superconducting films

This work determines the electron scattering rate in the a-b plane of epitaxial ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ films using two techniques. Infrared spectroscopy yields the scattering rate at temperatures of 10, 78, and 300 K by fitting reflectance data using thin-film optics and a model for the free-carrier conductivity. The scattering rate is also obtained using kinetic theory and an extrapolation of normal-state electrical resistivity data to superconducting temperatures based on the Bloch theory for the phonon-limited electrical resistivity of metals. The scattering rates determined using both techniques are in agreement and show that the electron mean free path in the a-b plane of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ superconducting films is three to four times the coherence length. Hence ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is pure but not in the extreme pure limit. An average defect interaction range of 4 nm is obtained using the defect density resulting from flux-pinning considerations.