Measurement of the absolute penetration depth and surface resistance of superconductors and normal metals with the variable spacing parallel plate resonator

Abstract

The variable spacing parallel plate resonator (VSPPR) is a microwave transmission line resonator with a continuously variable thickness of the dielectric spacer between the superconducting or metallic plates, filled by cryogenic liquid or vacuum. We measure the dielectric spacer thickness dependencies of the resonator frequency and quality factor, and fit them to theoretical forms, in order to extract the absolute values of penetration depth, λ, and surface resistance, Rs. A cryogenic micropositioning setup is developed to vary the spacer thickness from 0 to 100 μm with a resolution of 8.5 nm, and to maintain parallelism of the resonator plates. Measurement of ac capacitance between the plates is utilized to directly determine the separation between the resonator plates and to reduce the effect of their tilt and nonflatness on the accuracy of the measured Rs and λ. Because the operating temperature is fixed (77 K), the result for a superconductor is independent of an a priori model for the penetration depth versus temperature. This technique can also be employed as a surface impedance standard for characterization of high temperature superconducting films for microwave applications.