Microwave response of thin niobium films under perpendicular static magnetic fields

Abstract

The microwave response of high quality niobium films in a perpendicular static magnetic field has been investigated. The complex frequency shift was measured up to the upper critical fields. The data have been analyzed by the effective conductivity model for the type-II superconductors in the mixed state. This model is found to yield consistent results for the coherence lengths in high-κ superconducting samples, and can be used with HTSC even at temperatures much below Tc. It is shown that for samples with high values of depinning frequency, one should measure both components of the complex frequency shift in order to determine the flow resistivity.The thick Nb film (160 nm) has low resistivity at 10 K, comparable to the best single crystals, and low κ value. In contrast, the thinnest (10 nm) film has κ ≈ 9.5 and exhibits a high depinning frequency (≈ 20 GHz). The upper critical field determined from microwave measurements is related to the radius of nonoverlaping vortices, and appears to be larger than the one determined by the transition to the normal state.

Determination of coordinate dependence of a pinning potential from a microwave experiment with vortices

“…However, for the experiment it is crucial to adequately superimpose the applied currents and then to uncouple the picked-up dc and microwave signals maintaining that the line and the sample impedances be matching. Quantitatively, experimentally estimated values of the depinning frequency in the absence of a dc current and at a temperature of about 0.6T c are x p % 7 GHz for a 20 nm-thick 7 and a 40 nm-thick 8 Nb films. This value is strongly suppressed with the increase of both the field magnitude and the film thickness.…”

“…The appearance of experimental works utilizing the usual four-point scheme, 4 strip-line coplanar waveguides (CPWs), 5 Corbino geometry, 6,7 or the cavity method 8 to investigate the microwave vortex response in as-grown thin-film superconductors (or in those containing some nano-tailored pinning potential (PP) landscape) in the recent years reflects the explosively growing interest in the subject. In fact, such artificially fabricated pinning nanostructures provide a PP of unknown shape that requires certain assumptions concerning its coordinate dependence in order to fit the measured data.…”

Microwave Absorption by Vortices in Superconductors with a Washboard Pinning Potential

“…However, one of most crucial issues for the experiment is to adequately superimpose the applied currents and then, to uncouple the picked-up dc and microwave signals maintaining the matching of the impedances of the line and the sample. Quantitatively, experimentally estimated values of the depinning frequency in the absence of a dc current at a temperature of about 0.6T c are ω p ≈ 7 GHz for a 20 nm-thick [45] and a 40 nm-thick [46] Nb films. This value is strongly suppressed with increase of both, the field magnitude and the film's thickness.…”

“…The multitude of experimental works published recently utilizing the usual four-point scheme [42], strip-line coplanar waveguides (CPWs) [43], the Corbino geometry [44,45], or the cavity method [46] to investigate the microwave vortex response in as-grown thin-film superconductors or in those containing some nano-tailored PP landscape reflects the explosively growing interest in the subject. In connection with this, from the microwave power absorption further insight into the pinning mechanisms can be gained.…”

Noise-Assisted Microwave Up-conversion by Vortices in Thin-Film Superconductors with a dc-Biased Washboard Pinning Potential

“…In the absence of a dc drive, ω p separates the low-frequency regime, where the pinning forces dominate and the non-linear impedance Z(ω) is mainly nondissipative, from the high-frequency regime where the frictional forces dominate and Z(ω) is dissipative [2]. Quantitatively, an experimentally estimated value of ω p in the absence of a dc current at a temperature of 0.6T c is ω p ≈ 7 GHz for a 20 nm-thick [17] or a 40 nm-thick [18] Nb film. For comparison, in YBCO ω p < 15 GHz, typically [1].…”