A set of highly sensitive cavity perturbation techniques, quite different from the ones most commonly used to measure thin films, has been developed for measuring the surface impedance of small crystals of high-${\mathit{T}}_{\mathit{c}}$ superconductors. Since the results of these studies differ markedly from most surface-impedance measurements of thin films of high-${\mathit{T}}_{\mathit{c}}$ superconductors, we describe the techniques in detail, including recent improvements. Measurements of the surface resistance and penetration depth of a twin-free crystal of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ indicate two striking differences from the surface impedance of conventional superconductors. Both quantities exhibit linear temperature dependence at low temperatures rather than the exponentially activated behavior of an s-wave BCS superconductor. Also, a broad peak in the temperature dependence of the surface resistance indicates that the large transport scattering rate in the normal state collapses below ${\mathit{T}}_{\mathit{c}}$ as the holes condense into the superconducting condensate. Systematic studies of the influence of Zn and Ni impurities on the surface impedance indicate that these properties are very sensitive to defects and this sensitivity provides further insight into the pairing state. Although both types of impurities provide strong elastic scattering that limits the collapse of the scattering rate and suppresses the peak in the surface resistance, only Zn has a strong pair-breaking effect. As little as 0.31% Zn substitution makes ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ gapless, but Ni, which is a magnetic impurity has no such pair-breaking effect up to 0.75% substitution. This difference is the opposite of that expected for an s-wave BCS superconductor.

• Received 29 November 1993

DOI:https://doi.org/10.1103/PhysRevB.50.4051