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arXiv:1804.00856 · Applied Physics Letters

Radiofrequency generation by coherently moving fluxons

Oleksandr V. Dobrovolskiy, Roland Sachser, Michael Huth, Valerij A. Shklovskij, Руслан Володимирович Вовк, Volodymyr M. Bevz, M. I. Tsindlekht

Published Apr 9, 2018• 31 citations
arXivHTMLPDF

Abstract

A lattice of Abrikosov vortices in type II superconductors is characterized by a periodic modulation of the magnetic induction perpendicular to the applied magnetic field. For a coherent vortex motion under the action of a transport current, the magnetic induction at a given point of the sample varies in time with a washboard frequency fWB = v/d, where v is the vortex velocity and d is the distance between the vortices in the direction of motion. Here, by using a spectrum analyzer connected to a 50 nm-wide Au nanowire meander near the surface of a superconducting Nb film, we detect an ac voltage induced by coherently moving fluxons. The voltage is peaked at the washboard frequency, fWB, and its subharmonics, fTOF = fWB/5, determined by the antenna width. By sweeping the dc current value, we reveal that fWB can be tuned from 100 MHz to 1.5 GHz, thereby demonstrating that patterned normal metal/superconductor nanostructures can be used as dc-tunable generators operating in the radiofrequency range.

DOI
10.1063/1.5028213

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A lattice of Abrikosov vortices in type II superconductors is characterized by a periodic modulation of the magnetic induction perpendicular to the applied magnetic field. For a coherent vortex motion under the action of a transport current, the magnetic induction at a given point of the sample varies in time with a washboard frequency fWB = v/d, where v is the vortex velocity and d is the distance between the vortices in the direction of motion. Here, by using a spectrum analyzer connected to a 50 nm-wide Au nanowire meander near the surface of a superconducting Nb film, we detect an ac voltage induced by coherently moving fluxons. The voltage is peaked at the washboard frequency, fWB, and its subharmonics, fTOF = fWB/5, determined by the antenna width. By sweeping the dc current value, we reveal that fWB can be tuned from 100 MHz to 1.5 GHz, thereby demonstrating that patterned normal metal/superconductor nanostructures can be used as dc-tunable generators operating in the radiofrequency range.
We introduce a fluxonic metamaterial on the basis of nanopatterned superconducting Nb microstrips and employ it for modulation and synthesis of quantized loss levels in the lower GHz range by a sine-wave quasistatic ac drive. The nanopatterns are uniaxial nanogrooves with identical and different slope steepness, which induce a pinning potential of the washboard type for Abrikosov vortices. For the fundamental matching field, when the location of vortex rows geometrically matches the nanogrooves, the following effects are observed: The forward transmission coefficient S21(f) of the microstrips can be controllably modulated within a range of about 3 dB by the ac. For the sample with symmetric grooves, depending on the choice of the operation point in the current-voltage curve, the shape and the duty cycle of the output signal can be tuned. For the sample with asymmetric grooves, depending on the ac amplitude, a sine-to-triangular or a sine-to-rectangular pulse shape conversion is observed. The possibility of synthesizing quantized loss levels by a serial connection of the two samples with different nanopatterns is exemplified and can be used for the development of multilevel excess-loss-based fluxonic devices.
Superconductors are characterized by macroscopic phase coherence and have enabled cryogenic electronics and quantum technologies. Recent advances in 3D nanofabrication now offer possibilities for tuning functional properties relevant for on-chip 3D integration of superconductors. However, nonequilibrium phenomena in 3D nanostructures exposed to transport currents remain largeley unexplored. Here, we employ numerical simulations to investigate phase slipsdiscrete 2π jumps in the phase of the superconducting order parameterin a tubular Nb superconductor with a central constriction, which is subjected to both direct current (DC) and alternating current (AC) transport currents. We find that under DC drive, the system stabilizes periodic phase slips, resulting in GHz voltage oscillations. Introducing an additional AC frequency modulation generates microwave frequency combs which depend characteristically on the interaction between moving vortices and phase slips. Our findings open avenues for developing on-chip frequency comb generators in 3D cryoelectronics.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.
We describe a new method for observing magnetic periodicities, both spatial and temporal, ultimately capable of resolving wavelengths between 100 and 105{10}^{5}105 \AA{} and frequencies between 0.5 and 500 MHz. We have used this method to observe the periodic magnetic field above the surface of a type-II superconductor containing a lattice of flux lines which moves under transport currents. We believe that the measurements are the first direct observations of the flux-flow velocity in a type-II superconductor.
We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.
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–14 GHz at different temperatures, magnetic fields, and dc values. The microwave loss is most effectively reduced when the Abrikosov vortex lattice spatially matches the underlying washboard pinning landscape. The forward transmission coefficient S21(f) of the microstrip has a dc-tunable cut-off frequency fd 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.