Dual cut-off direct current-tunable microwave low-pass filter on superconducting Nb microstrips with asymmetric nanogrooves

Abstract

We present a dual cut-off, dc-tunable low-pass microwave filter on a superconducting Nb microstrip with uniaxial asymmetric nanogrooves. The frequency response of the device was measured in the range 300 KHz to 14 GHz at different temperatures, magnetic fields, and dc current values. The microwave loss is most effectively reduced when the Abrikosov vortex lattice spatially matches the underlying washboard pinning landscape. The forward transmission coefficient S 21 (f ) of the microstrip has a dc-tunable cut-off frequency f d which notably changes under dc bias reversal, due to the two different slope steepnesses of the pinning landscape. The device's operation principle relies upon a crossover from the weakly dissipative response of vortices at low frequencies when they are driven over the grooves, to the strongly dissipative response at high frequencies when the vortices are oscillating within one groove. The filter's cut-off frequency is the vortex depinning frequency tunable by the dc bias as it diminishes the pinning effect induced by the nanopattern. The reported results unveil an advanced microwave functionality of superconducting films with asymmetric (ratchet) pinning landscapes and are relevant for tuning the microwave loss in superconducting planar transmission lines.

Abrikosov fluxonics in washboard nanolandscapes

“…In the absence of a dc bias, the mw loss is maximal at high frequencies, whereas the vortex response is weakly dissipative at low frequencies. For both dc bias polarities, upon increasing the dc value, the ∆S 21 curves shift towards lower frequencies but the magnitudes of the shifts substantially differ, as is in contrast with sample S [104]. The reduction of the depinning frequency upon increasing the dc bias can be understood as a consequence of the effective lowering of the pinning potential well due to its tilt by the dc current, see also Fig.…”

“…7(d) is plotted the zero-bias depinning frequencies at T = 0 and H = 0, f d (0, 0), for both samples [104] along with the data for Nb films reported in Refs. [18,105,106].…”

Thickness-modulated tungsten–carbon superconducting nanostructures grown by focused ion beam induced deposition for vortex pinning up to high magnetic fields

“…In order to design vortex-pinning landscapes, electron beam lithography is commonly used to fabricate arrays of holes [33,40] or arrays of magnetic dots/lines [30,34,36,39,41], whereas selective ion implantation [29,38,41] and insertion of structural defects [35,37,43] are other common pinning strategies. The use of a focused ion beam (FIB) for enhanced vortex pinning through local removal of the superconducting material has been explored as well [40,42,46–48]. In contrast to our approach followed here, such previous work has focused on the use of FIB for milling instead of deposition and the pinning has not been observed up to high magnetic fields, as it was for our case.…”

Orientational ordering, buckling, and dynamic transitions for vortices interacting with a periodic quasi-one-dimensional substrate

“…In general, the colloidal studies focused on the case where the particle lattice constant a is larger than the substrate lattice constant w. Martinoli et al investigated vortex pinning in samples with a 1D periodic thickness modulation [53][54][55] and observed broad commensuration peaks in the depinning threshold that were argued to be correlated with the formation of ordered vortex arrangements that could align with the substrate periodicity. Other vortex studies in similar samples also revealed peaks in the critical depinning force associated with commensuration effects 56,57 , while studies of vortices interacting with 1D magnetic strips showed that commensurate conditions were marked by depinning steps rather than peaks 58 . Under an applied dc drive, depinning transitions occur into a sliding state, and when an additional ac drive is added to the dc drive, a series of Shapiro steps in the voltage-current curves appears when the frequency of the oscillatory motion of the vortex lattice moving over the periodic substrate locks with the ac driving frequency 54 .…”

“…For F p = 0.1 the zig-zag state transitions into a hexagonal lattice and the peak in F c begins to disappear. Some experiments examining vortices in q1D periodic pinning structures show that peaks in the critical current occur at certain fillings 53,[55][56][57] in regimes where the pinning is weak, whereas other experiments performed in the strong pinning limit reveal more step-like features in the critical current. This suggests that the experiments in the strong pinning limit are producing buckling transitions 58 .…”