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Planar superconducting microwave resonators are key elements in a variety oftechnical applications and also act as sensitive probes for microwavespectroscopy of various materials of interest. Here superconducting Pb is asuitable material as a basis for microwave stripline resonators.  To utilize Pb stripline resonators in a variable magnetic field (e.g. inESR), the electrodynamics of such resonators in finite magnetic field has to bewell understood. Therefore we performed microwave transmission measurements onsuperconducting Pb stripline resonators in a variable, parallel magnetic field.We determined surface resistance, penetration depth as well as real andimaginary parts, \sigma$_1$ and \sigma$_2$, of the complex conductivity ofsuperconducting Pb as a function of magnetic field. Here we find featuresreminiscent of those in temperature-dependent measurements, such as a maximumin \sigma$_1$ (coherence peak). At magnetic fields above the critical field ofthis type-I superconductor we still find low-loss microwave response, which weassign to remaining superconductivity in the form of filaments within the Pb.Hysteresis effects are found in the quality factor of resonances once the sweptmagnetic field has exceeded the critical magnetic field. This is due to normalconducting areas that are pinned and can therefore persist in thesuperconducting phase. Besides zero-field-cooling we show an alternative way toeliminate these even at T<T$_c$. Based on our microwave data, we determine thecritical magnetic field and the critical temperature of Pb in a temperaturerange between 1.6K and 6.5K and magnetic fields up to 140mT, showing goodagreement with BCS predictions. We study a Sn sample in a Pb resonator todemonstrate the applicability of superconducting Pb stripline resonators in theexperimental study of other (super-)conducting materials in a variable magneticfield.

Superconducting Pb stripline resonators in parallel magnetic field and their application for microwave spectroscopy