Effect of a temperature dependent effective quasiparticle mass on the surface impedance of YBa ₂ Cu ₃ O _7-x

Abstract:

The temperature dependent surface impedance Z _s ( T ) of single-crystalline YBa ₂ Cu ₃ O _7-x (YBCO) was analyzed within the two-fluid model in terms of the fraction of paired charge carriers, f _s ( T ), and of the quasiparticle scattering time. The usual approach was extended by considering a temperature dependent effective quasiparticle mass m ^* ( T ), which results from a strong electron-phonon interaction. This effect must not be neglected in the description of high-temperature superconductors due to the large ratio of T _c to the Debye temperature T _D . The temperature dependence of the penetration depth, of high-quality YBCO crystals and films could be described with an electron-phonon coupling constant, and using f _s ( T ) = 1- ( T / T _c ) ^2.8 as an approximation of the BCS theory. Different trial phonon spectra were encountered in terms of their ability to reproduce the -data. The scattering time was described by the Bloch-Grüneisen formalism with T _D =460 K. Assuming an Einstein spectrum with, a residual resistivity and a fraction of unpaired quasiparticles at T = 0 K yielded a surprisingly good agreement of the model with Z _s ( T )-data measured at 87 GHz with a high-quality epitaxial YBCO film between T =4 K and T _c . While an exact reproduction of the surface impedance asks for a rigorous theoretical computation, our analysis demonstrates that strong electron-phonon coupling is relevant for discussing the unconventional transport properties of YBCO.