Electrodynamic properties of oxide superconductors

The electrodynamic properties of oxide high temperature superconductors are reviewed. Most of the experimental data are from thin films and bulk single crystals of YBa$_{2}$Cu$_{3}$O$_{7-x}$, which - together with thin films of thallium-based oxide uperconductors provide the lowest microwave losses making epitaxially grown thin films attractive for applications in microwave technology. Among the various techniques for the determination of the electrodynamic response of superconducting thin filmscavity, dielectric, and planar resonators are the most successful ones for the frequencyrange from 1 to 100 GHz. For the millimeter and submillimeter wave range nonresonant transmission techniques in frequency and time domain have been used successfully. Bulk single crystals have been studied by various types of cavity perturbationtechniques. YBa$_{2}$Cu$_{3}$O$_{7-x}$ bulk single crystals and epitaxial thin films exhibit a steep drop ofthe surface resistance R$_{s}$ just below the transition temperature T$_{c}$, to values at 77 K which are about 300 $\mu \Omega$ at 10 GHz. The observed dependence on the frequency fcan be described by f$^{A}$ with sample-dependent A values between 1.5 and 2. At lower temperatures R$_{s}$ (T) is substantially different both from that predicted by BCS theoryand observed experimentally for conventional superconductors. Typically, R$_{s}$ (T) exhibits a plateau between 30 and 70 K corresponding to a frequency-dependent maxirnurnin the real part of the conductivity. The observed correlation of the height of this maximum to the defect density indicates that above about 30 K the electrodynamicresponse is dominated by a strong decrease of the quasiparticle lifetime just below T$_{c}$. Below T$_{c}$/2 the situation is still quite unclear. The observed temperaturedependences both for R$_{s}$ and the London penetration depth $\lambda_{L}$ range from weak exponential corresponding to energy gaps more than two times smaller than expectedfrom weak-coupling BCS theory over quadratic to linear dependences. In any case, a high residual surface resistance R$_{res}$ = R$_{s}$(T $\rightarrow$ 0) remains. In particular, the lowtemperature regime was found to be strongly affected by the amount and ordering of oxygen vacancies in the copper-oxygen chains. The active rote of the copper-oxygenchains as a conducting subsystem was worked out theoretically within a strongcoupling theory based on phonon-mediated superconductivity and can quantitativelyexplain some of the observed results. In particular, gapless superconductivity can be easily achieved from magnetic pair breaking in the copper-oxygen chains. $\textit{d}$-wave superconductivity, as expected for superconductivity mediated by spin fluauationsinstead of phonons, leads to a gapless behavior as well. The observed temperature dependences of $\lambda_{L}$ and R$_{s}$ can be explained to some extent within $\textit{d}$-wave models.In contradiction to the hole doped cuprates (as e.g. YBa$_{2}$Cu$_{3}$O$_{7-x}$), the electron doped cuprates exhibit an electromagnetic response which is similar to predictionsfor an isotropic s-wave order parameter