Crossover from dirty to clean superconducting limit in dc magnetron-sputtered thin Nb films

High-quality Nb (110) thin films with residual resistance ratios up to 60 and critical temperatures Tc≈9.27 K have been prepared by conventional dc-magnetron sputtering on α-Al2O3 by careful selection of the sputtering conditions. This allowed for a systematic study of the influence of the growth rate on the structural quality and the superconducting properties of the films. The optimized growth conditions were revealed at the substrate temperature Ts=850 °C, Ar pressure Ps=0.4 Pa, and the growth rate g≃0.5 nm/s. The results of the films' structural characterization by X-ray diffraction, reflection high-energy electron diffraction, and atomic force microscopy are presented. In terms of the electron mean free path l and the superconducting coherence length ξ, deduced from the magneto-resistivity data, the clean superconducting limit (l>ξ) is realized in the high-purity films. For comparison, in impure Nb films sputtered at room temperature while keeping the rest of the sputtering parameters unvaried, the opposite dirty limit (ξ≳l) ensues. The merits of these findings are discussed in the context of the demands of present-day fluxonics devices regarding the normal-state and flux-flow properties of superconducting films they are made of

Current-controlled filter on superconducting films with a tilted washboard pinning potential

The influence of an ac current of arbitrary amplitude and frequency on the mixed-state dc-voltage-ac-drive tiltingratchet response of a superconducting film with uniaxial cosine pinning potential at finite temperature is theoretically investigated. The results are obtained in the single-vortex approximation, within the frame of an exact solution of the Langevin equation for non-interacting vortices. Both experimentally achievable, the dc ratchet response and absorbed ac power are predicted to demonstrate a pronounced filter-like behavior at microwave frequencies. Based on our findings, we propose a cut-off filter and discuss its operating curves as functions of the driving parameters, i.e, ac amplitude, frequency, and dc bias. The predicted results can be examined, e.g, on superconducting films with a washboard pinning potential landscape

Current-controlled filter on superconducting films with a tilted washboard pinning potential

The influence of an ac current of arbitrary amplitude and frequency on the mixed-state dc-voltage-ac-drive tiltingratchet response of a superconducting film with uniaxial cosine pinning potential at finite temperature is theoretically investigated. The results are obtained in the single-vortex approximation, within the frame of an exact solution of the Langevin equation for non-interacting vortices. Both experimentally achievable, the dc ratchet response and absorbed ac power are predicted to demonstrate a pronounced filter-like behavior at microwave frequencies. Based on our findings, we propose a cut-off filter and discuss its operating curves as functions of the driving parameters, i.e, ac amplitude, frequency, and dc bias. The predicted results can be examined, e.g, on superconducting films with a washboard pinning potential landscape

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

So far the main theoretical basis for understanding and optimization of the microwave properties of vortices in type II superconductors has been relying upon the Coffey–Clem (CC) approach for the linear impedance at nonzero temperature. However, the CC model does not account for the non-linear response and the possibility to control it by changing the value of the dc transport current in a superconducting sample. For this reason, we have exactly solved the Langevin equation for the two-dimensional nonlinear vortex dynamics in a dc bias-tilted cosine pinning potential in the presence of an ac current of arbitrary amplitude and frequency ω and have, thereby, substantially generalized the CC results. In this work we analyze the behavior of the non-linear response on kω-frequency in a wide range of dc and ac current densities, ω, and temperature. The kω- response is found to depend strongly on all these parameters, as exemplified for the third-harmonic (k = 3) transformation coefficient Z3. The parametric window for the most enhanced up-conversion is presented. The predicted effects can be experimentally verified in thin-film superconductors with some pinning potential of the washboard type

Fluxonic Properties of Vortices in a Washboard Pinning Potential Fabricated by Focused Particle Beam Techniques

A challenging aspect of the usage of patterned nanostructures relates to the development of superconducting devices operating with the Abrikosov vortices in some pinning potential. To provide such a potential we have used thin epitaxial films of Nb with washboard-like nanostructures in the form of grooves or Co stripes. The nanostructures were prepared by focused ion beam milling or focused electron beam induced deposition, respectively. The results of transport measurements affirm the existence of two fluxonic effects, the guided vortex motion and the vortex ratchet effect, both invoked by the nanostructuring. In particular, the effects represent the basis for the development of advanced fluxonic devices using a directional or orientational control of the net vortex motion in Nb films nanostructured by focused particle beam techniques

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

The measurement of the complex impedance response and accompanied power absorption P(ω) in the radiofrequency and microwave ranges represents a most popular experimental method to investigate pinning mechanisms and the vortex dynamics in type-II superconductors. In the theory, the pinning potential (PP) well for a vortex must be a priori specified in order to subsequently analyze the measured data. We have theoretically solved the inverse problem at T = 0 K and exemplify how the coordinate dependence of a PP can be determined from a set of experimental curves P(ω|j₀) measured at subcritical dc currents 0 < j₀ < jc under a small microwave excitation j₁ << jc with frequency ω. We furthermore elucidate how and why the depinning frequency ωp, which separates the non-dissipative (quasi-adiabatic) and the dissipative (high-frequency) regimes of small vortex oscillations in the PP, is reduced with the increase of j₀. The results can be directly applied to a wide range of conventional superconductors with a PP subjected to superimposed dc and small microwave ac currents at T << Tc

Material composition – Pinning strength correlation in Nb thin films with focused ion beam-milled washboard nanostructures

An analysis of the interrelated changes in the material composition and the pinning strength in nanostructured Nb (110) thin films is presented. The nanopatterns were prepared by focused ion beam milling of an array of uniaxial grooves. They induce a washboard-like pinning potential landscape for vortices in the mixed state. By applying different magnetic fields, the most likely pinning sites along which the flux lines move through the samples have been selected. By this, either the background isotropic pinning of the pristine film or the enhanced isotropic pinning originating from the nanoprocessing has been probed. The enhanced pinning strength in the processed films has been found to correlate with the content of Ga implanted into the films during the nanopatterning

Electrical transport and pinning properties of Nb thin films patterned with focused ion beam-milled washboard nanostructures

A careful analysis of the magneto-transport properties of epitaxial nanostructured Nb thin films in the normal and the mixed state is performed. The nanopatterns were prepared by focused ion beam (FIB) milling. They provide a washboard-like pinning potential landscape for vortices in the mixed state and simultaneously cause a resistivity anisotropy in the normal state. Two matching magnetic fields for the vortex lattice with the underlying nanostructures have been observed. By applying these fields, the most likely pinning sites along which the flux lines move through the samples have been selected. By this, either the background isotropic pinning of the pristine film or the enhanced isotropic pinning originating from the nanoprocessing have been probed. Via an Arrhenius analysis of the resistivity data the pinning activation energies for three vortex lattice parameters have been quantified. The changes in the electrical transport and the pinning properties have been correlated with the results of the microstructural and topographical characterization of the FIB-patterned samples. Accordingly, along with the surface processing, FIB milling has been found to alter the material composition and the degree of disorder in as-grown films. The obtained results provide further insight into the pinning mechanisms at work in FIB-nanopatterned superconductors, e.g. for fluxonic applications

Crossover from dirty to clean superconducting limit in dc magnetron-sputtered thin Nb films

High-quality Nb (110) thin films with residual resistance ratios up to 60 and critical temperatures Tc≈9.27 K have been prepared by conventional dc-magnetron sputtering on α-Al2O3 by careful selection of the sputtering conditions. This allowed for a systematic study of the influence of the growth rate on the structural quality and the superconducting properties of the films. The optimized growth conditions were revealed at the substrate temperature Ts=850 °C, Ar pressure Ps=0.4 Pa, and the growth rate g≃0.5 nm/s. The results of the films' structural characterization by X-ray diffraction, reflection high-energy electron diffraction, and atomic force microscopy are presented. In terms of the electron mean free path l and the superconducting coherence length ξ, deduced from the magneto-resistivity data, the clean superconducting limit (l>ξ) is realized in the high-purity films. For comparison, in impure Nb films sputtered at room temperature while keeping the rest of the sputtering parameters unvaried, the opposite dirty limit (ξ≳l) ensues. The merits of these findings are discussed in the context of the demands of present-day fluxonics devices regarding the normal-state and flux-flow properties of superconducting films they are made of