Broadband Corbino spectroscopy and stripline resonators to study the microwave properties of superconductors

Abstract

Superconducting materials are of great interest both for the fundamental understanding of electrons in solids as well as for a range of different applications. Studying superconductors with microwaves offers a direct experimental access to the electrodynamic response of these materials, which in turn can reveal fundamental material properties such as the superconducting penetration depth. Here we describe two different techniques to study superconductors at microwave frequencies: the broadband Corbino approach can cover frequencies from the MHz range up to 50 GHz continuously but is limited to thin-film samples whereas the stripline resonators are sensitive enough to study low-loss single crystals but reveal data only at a set of roughly equidistant resonant frequencies. We document the applicability of these two techniques with data taken on an ultrathin TaN film and a single crystal of the heavy-fermion superconductor CeCu 2 Si 2 , respectively.

Microwave probing of bulk dielectrics using superconducting coplanar resonators in distant-flip-chip geometry

“…Planar superconducting microwave resonators play an important role in solid state research, including cryogenic spectroscopic studies. [11][12][13][14][15][16][17][18][19] One can simultaneously probe various harmonics of a fundamental resonance frequency and perform measurements at low temperatures, even in setups with limited space for the sample probe, such as in high magnetic fields or at mK temperatures. 14,[20][21][22][23][24] Superconducting resonators can reach very high quality factors 25 and thus high sensitivity for the dielectric under study.…”

Superconducting energy scales and anomalous dissipative conductivity in thin films of molybdenum nitride

“…The lesser of both scales determines T c . In order to address this question, we employ optical measurements in the THz frequency range which have turned out to be a powerful approach to access ∆ and J of thinfilm superconductors [21] as just one asset of optical spectroscopy in this context [22][23][24][25][26]. Our material of choice Overview of the parameters characterizing structural (film thickness d, grain diameter δ), free-electron (roomtemperature dc-resistivity ρ dc , Fermi wave-vector × electron mean free path kF ), and superconducting (critical temperature Tc, zero-temperature estimates of the energy gap 2∆(0), superfluid density ns(0), superfluid stiffness J(0), penetration depth λ(0), and the coupling ratio 2∆(0)/kBTc) properties of the MoN films under study.…”

Estimation of microwave resonant measurements uncertainty from uncalibrated data

“…Moreover, within the relatively large set of experimental curves (~ 40), it can be observed (Figure 3(b) and Figure 4(b) use the same legend as in the 'a' subfigures) that the discrepancy values have a balanced distribution around zero for both fit approaches. This feature calls for a closer investigation of the characteristic of this distribution, allowing us to go beyond a rough estimation of the error due to the use of uncalibrated curves as worst-case values only [10]. The latter yields, as an estimate of the maximum additional contribution to the measurement relative uncertainty, arising from the use of uncalibrated data (equal to 5.4 % for and to 16 ppm for 0 ), but we show below that the data supports a reduction of this figure.…”

“…Here, the main role is taken by the absence of microwave standards that are capable of maintaining their characteristics in a hostile environment. One possible solution is to develop custom standards [10], but this often requires very advanced techniques and specific expertise. Moreover, it is rather difficult to associate the appropriate uncertainty with the measured quantity.…”