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

Planar superconducting microwave resonators are key elements in a variety of technical applications and also act as sensitive probes for microwave spectroscopy of various materials of interest. Here superconducting Pb is a suitable material as a basis for microwave stripline resonators. To utilize Pb stripline resonators in a variable magnetic field (e.g. in ESR), the electrodynamics of such resonators in finite magnetic field has to be well understood. Therefore we performed microwave transmission measurements on superconducting Pb stripline resonators in a variable, parallel magnetic field. We determined surface resistance, penetration depth as well as real and imaginary parts, σ$_1$ and σ$_2$, of the complex conductivity of superconducting Pb as a function of magnetic field. Here we find features reminiscent of those in temperature-dependent measurements, such as a maximum in σ$_1$ (coherence peak). At magnetic fields above the critical field of this type-I superconductor we still find low-loss microwave response, which we assign to remaining superconductivity in the form of filaments within the Pb. Hysteresis effects are found in the quality factor of resonances once the swept magnetic field has exceeded the critical magnetic field. This is due to normal conducting areas that are pinned and can therefore persist in the superconducting phase. Besides zero-field-cooling we show an alternative way to eliminate these even at T<T$_c$. Based on our microwave data, we determine the critical magnetic field and the critical temperature of Pb in a temperature range between 1.6K and 6.5K and magnetic fields up to 140mT, showing good agreement with BCS predictions. We study a Sn sample in a Pb resonator to demonstrate the applicability of superconducting Pb stripline resonators in the experimental study of other (super-)conducting materials in a variable magnetic field.