Imaging of super-fast dynamics and flow instabilities of superconducting vortices

Quantum thermodynamics with a single superconducting vortex

We demonstrate complete control over dynamics of a single superconducting vortex in a nanostructure, which we coin the Single Vortex Box. Our device allows us to trap the vortex in a field-cooled aluminum nanosquare and expel it on demand with a nanosecond pulse of electrical current. Using the time-resolving nanothermometry we measure [Formula: see text] joules as the amount of the dissipated heat in the elementary process of the single-vortex expulsion. Our experiment enlightens the thermodynamics of the absorption process in the superconducting nanowire single-photon detectors, in which vortices are perceived to be essential for a formation of a detectable hotspot. The demonstrated opportunity to manipulate a single superconducting vortex reliably in a confined geometry comprises a proof of concept of a nanoscale nonvolatile memory cell with subnanosecond write and read operations, which offers compatibility with quantum processors based either on superconducting qubits or on rapid single-flux quantum circuits.

Anomalous behavior of critical current in a superconducting film triggered by DC plus terahertz current

The critical current in a superconductor (SC) determines the performance of many SC devices, including SC diodes which have attracted recent attention. Hitherto, studies of SC diodes are limited in the DC-field measurements, and their performance under a high-frequency current remains unexplored. Here, we conduct the first investigation on the interaction between the DC and terahertz (THz) current in a SC artificial superlattice. We found that the DC critical current is sensitively modified by THz pulse excitations in a nontrivial manner. In particular, at low-frequency THz excitations below the SC gap, the critical current becomes sensitive to the THz-field polarization direction. Furthermore, we observed anomalous behavior in which a supercurrent flows with an amplitude larger than the modified critical current. Assuming that vortex depinning determines the critical current, we show that the THz-current-driven vortex dynamics reproduce the observed behavior. While the delicate nonreciprocity in the critical current is obscured by the THz pulse excitations, the interplay between the DC and THz current causes a non-monotonic SC/normal-state switching with current amplitude, which can pave a pathway to developing SC devices with novel functionalities.

Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg-Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at α=0∘, vortices move paraxially in opposite directions within each half-tube; an increase in α displaces the areas with the close-to-maximum normal component |Bn| to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum fU(α). At lower B values, upon reaching the critical angle αc, the close-to-slit vortex chains disappear, yielding fU of the nf1 type (n≥1: an integer; f1: the vortex nucleation frequency). At higher B values, fU is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at α=90∘. In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields.

Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress

Superconductor-insulator/metal transition (SMT) as a paradigm of quantum phase transition has been a research highlight over the last three decades. Benefit from recent developments in the fabrication and measurements of two-dimensional (2D) superconducting films and nanodevices, unprecedented quantum phenomena have been revealed in the quantum phase transitions of 2D superconductors. In this review, we introduce the recent progress on quantum phase transitions in 2D superconductors, focusing on the quantum Griffiths singularity (QGS) and anomalous metal state. Characterized by a divergent critical exponent when approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline Ga films and subsequently detected in various 2D superconductors. The universality of QGS indicates the profound influence of quenched disorder on quantum phase transitions. Besides, in a 2D superconducting system, whether a metallic ground state can exist is a long-sought mystery. Early experimental studies indicate an intermediate metallic state in the quantum phase transition of 2D superconductors. Recently, in high-temperature superconducting films with patterned nanopores, a robust anomalous metal state (i.e. quantum metal or Bose metal) has been detected, featured as the saturated resistance in the low temperature regime. Moreover, the charge-2equantum oscillations are observed in nanopatterned films, indicating the bosonic nature of the anomalous metal state and ending the debate on whether bosons can exist as a metal. The evidences of the anomalous metal states have also been reported in crystalline epitaxial thin films and exfoliated nanoflakes, as well as granular composite films. High quality filters are used in these works to exclude the influence of external high frequency noises in ultralow temperature measurements. The observations of QGS and metallic ground states in 2D superconductors not only reveal the prominent role of quantum fluctuations and dissipations but also provide new perspective to explore quantum phase transitions in superconducting systems.

Flux focusing with a superconducting nanoneedle for scanning SQUID susceptometry

A nanofabricated superconducting quantum interference device (nano-SQUID) is a direct and sensitive flux probe used for magnetic imaging of quantum materials and mesoscopic devices. Due to the functionalities of superconductive integrated circuits, nano-SQUIDs fabricated on chips are particularly versatile, but their spatial resolution has been limited by their planar geometries. Here, we use femtosecond laser 3-dimensional (3D) lithography to print a needle onto a nano-SQUID susceptometer to overcome the limits of the planar structure. The nanoneedle coated with a superconducting shell focused the flux from both the field coil and the sample. We performed scanning imaging with such a needle-on-SQUID (NoS) device on superconducting test patterns with topographic feedback. The NoS showed improved spatial resolution in both magnetometry and susceptometry relative to the planarized counterpart. This work serves as a proof-of-principle for integration and inductive coupling between superconducting 3D nanostructures and on-chip Josephson nanodevices.

Chip-Integrated Vortex Manipulation

The positions of Abrikosov vortices have long been considered as means to encode classical information. Although it is possible to move individual vortices using local probes, the challenge of scalable on-chip vortex-control remains outstanding, especially when considering the demands of controlling multiple vortices. Realization of vortex logic requires means to shuttle vortices reliably between engineered pinning potentials, while concomitantly keeping all other vortices fixed. We demonstrate such capabilities using Nb loops patterned below a NbSe₂ layer. SQUID-on-Tip (SOT) microscopy reveals that the loops localize vortices in designated sites to a precision better than 100 nm; they realize "push" and "pull" operations of vortices as far as 3 μm. Successive application of such operations shuttles a vortex between adjacent loops. Our results may be used as means to integrate vortices in future quantum circuitry. Strikingly, we demonstrate a winding operation, paving the way for future topological quantum computing and simulations.

Direct observation of a superconducting vortex diode

The interplay between magnetism and superconductivity can lead to unconventional proximity and Josephson effects. A related phenomenon that has recently attracted considerable attention is the superconducting diode effect, in which a nonreciprocal critical current emerges. Although superconducting diodes based on superconductor/ferromagnet (S/F) bilayers were demonstrated more than a decade ago, the precise underlying mechanism remains unclear. While not formally linked to this effect, the Fulde-Ferrell-Larkin-Ovchinikov (FFLO) state is a plausible mechanism due to the twofold rotational symmetry breaking caused by the finite center-of-mass-momentum of the Cooper pairs. Here, we directly observe asymmetric vortex dynamics that uncover the mechanism behind the superconducting vortex diode effect in Nb/EuS (S/F) bilayers. Based on our nanoscale SQUID-on-tip (SOT) microscope and supported by in-situ transport measurements, we propose a theoretical model that captures our key results. The key conclusion of our model is that screening currents induced by the stray fields from the F layer are responsible for the measured nonreciprocal critical current. Thus, we determine the origin of the vortex diode effect, which builds a foundation for new device concepts.

Causes and Consequences of Ordering and Dynamic Phases of Confined Vortex Rows in Superconducting Nanostripes

Understanding the behaviour of vortices under nanoscale confinement in superconducting circuits is important for the development of superconducting electronics and quantum technologies. Using numerical simulations based on the Ginzburg-Landau theory for non-homogeneous superconductivity in the presence of magnetic fields, we detail how lateral confinement organises vortices in a long superconducting nanostripe, presenting a phase diagram of vortex configurations as a function of the stripe width and magnetic field. We discuss why the average vortex density is reduced and reveal that confinement influences vortex dynamics in the dissipative regime under sourced electrical current, mapping out transitions between asynchronous and synchronous vortex rows crossing the nanostripe as the current is varied. Synchronous crossings are of particular interest, since they cause single-mode modulations in the voltage drop along the stripe in a high (typically GHz to THz) frequency range.

Direct observation of vortices in an electron fluid

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance^1-4, higher-than-ballistic conduction^5-7, Poiseuille flow in narrow channels^8-10 and violation of the Wiedemann-Franz law¹¹. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip¹², we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe₂. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Topological transitions in ac/dc-driven superconductor nanotubes

Extending of nanostructures into the third dimension has become a major research avenue in condensed-matter physics, because of geometry- and topology-induced phenomena. In this regard, superconductor 3D nanoarchitectures feature magnetic field inhomogeneity, non-trivial topology of Meissner currents and complex dynamics of topological defects. Here, we investigate theoretically topological transitions in the dynamics of vortices and slips of the phase of the order parameter in open superconductor nanotubes under a modulated transport current. Relying upon the time-dependent Ginzburg–Landau equation, we reveal two distinct voltage regimes when (i) a dominant part of the tube is in either the normal or superconducting state and (ii) a complex interplay between vortices, phase-slip regions and screening currents determines a rich FFT voltage spectrum. Our findings unveil novel dynamical states in superconductor open nanotubes, such as paraxial and azimuthal phase-slip regions, their branching and coexistence with vortices, and allow for control of these states by superimposed dc and ac current stimuli.

Multi-Steps Magnetic Flux Entrance/Exit at Thermomagnetic Avalanches in the Plates of Hard Superconductors

Avalanche cascades of magnetic flux have been detected at thermomagnetic instability of the critical state in the plates of Nb-Ti alloy. It was found that, the magnetic flux Φ enters conventional superconductor in screening regime and leaves in trapping regime in the form of a multistage "stairways", with the structure dependent on the magnetic field strength and magnetic history, with approximately equal successive portions ΔΦ in temporal Φ(t) dependence, and with the width depending almost linearly on the plate thickness. The steady generation of cascades was observed for the full remagnetization cycle in the field of 2-4 T. The structure of inductive signal becomes complex already in the field of 0-2 T and it was shown, on the base of Fourier analysis, that, the avalanche flux dynamic produces, in this field range, multiple harmonics of the electric field. The physical reason of complex spectrum of the low-field avalanche dynamics can be associated with rough structure of moving flux front and with inhomogeneous relief of induction. It was established that the initiation of cascades occurs mainly in the central part of the lateral surface. The mechanism of cascades generation seems to be connected to the "resonator's properties" of the plates.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Sagnac interferometer for time-resolved magneto-optical measurements

We introduce a time-resolved magneto-optical measurement technique based on a zero-area Sagnac interferometer. By replacing a continuous wave light source to a pulsed one, temporal resolution of hundreds of picoseconds is achieved. Because two lights passing through a Sagnac loop always travel the same optical path length, the interference from the phase modulation and Kerr rotation occurs in a pulse mode. For illustration of the apparatus, we present ferromagnetic resonance of a Permalloy film caused by a magnetic field pump. The instrument still possesses the favorable properties of a Sagnac interferometer, such as rejection of all the reciprocal effects, and shows 1μrad/Hz sensitivity at a 3 µW optical power in the pulse mode.

Lateral Josephson Junctions as Sensors for Magnetic Microscopy at Nanoscale

Lateral Josephson junctions (LJJ) made of two superconducting Nb electrodes coupled by Cu-film are applied to quantify the stray magnetic field of Co-coated cantilevers used in magnetic force microscopy (MFM). The interaction of the magnetic cantilever with LJJ is reflected in the electronic response of LJJ as well as in the phase shift of cantilever oscillations, simultaneously measured. The phenomenon is theorized and used to establish the spatial map of the stray field. Based on our findings, we suggest integrating LJJs directly on the tips of cantilevers and using them as nanosensors of local magnetic fields in scanning probe microscopes. Such probes are less invasive than conventional magnetic MFM cantilevers and simpler to realize than SQUID-on-tip sensors.

In situ transport characterization of magnetic states in Nb/Co superconductor/ferromagnet heterostructures

Employment of the non-trivial proximity effect in superconductor/ferromagnet (S/F) heterostructures for the creation of novel superconducting devices requires accurate control of magnetic states in complex thin-film multilayers. In this work, we study experimentally in-plane transport properties of microstructured Nb/Co multilayers. We apply various transport characterization techniques, including magnetoresistance, Hall effect, and the first-order-reversal-curves (FORC) analysis. We demonstrate how FORC can be used for detailed in situ characterization of magnetic states. It reveals that upon reduction of the external field, the magnetization in ferromagnetic layers first rotates in a coherent scissor-like manner, then switches abruptly into the antiparallel state and after that splits into the polydomain state, which gradually turns into the opposite parallel state. The polydomain state is manifested by a profound enhancement of resistance caused by a flux-flow phenomenon, triggered by domain stray fields. The scissor state represents the noncollinear magnetic state in which the unconventional odd-frequency spin-triplet order parameter should appear. The non-hysteretic nature of this state allows for reversible tuning of the magnetic orientation. Thus, we identify the range of parameters and the procedure for in situ control of devices based on S/F heterostructures.

Skyrmion-(Anti)Vortex Coupling in a Chiral Magnet-Superconductor Heterostructure

We report experimental coupling of chiral magnetism and superconductivity in [IrFeCoPt]/Nb heterostructures. The stray field of skyrmions with radius ≈50  nm is sufficient to nucleate antivortices in a 25 nm Nb film, with unique signatures in the magnetization, critical current, and flux dynamics, corroborated via simulations. We also detect a thermally tunable Rashba-Edelstein exchange coupling in the isolated skyrmion phase. This realization of a strongly interacting skyrmion-(anti)vortex system opens a path toward controllable topological hybrid materials, unattainable to date.

Moving Pearl Vortices in Thin-Film Superconductors

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

Nonmonotonic Temperature-Dependent Dissipation at Nonequilibrium in Atomically Thin Clean-Limit Superconductors

Resistance in superconductors arises from the motion of vortices driven by flowing supercurrents or external electromagnetic fields and may be strongly affected by thermal or quantum fluctuations. The common expectation is that as the temperature is lowered, vortex motion is suppressed, leading to a decreased resistance. We show experimentally that in clean-limit atomically thin 2H-NbSe₂ the resistance below the superconducting transition temperature may be nonmonotonic, passing through a minimum before increasing again as the temperature is decreased further. The effect is most pronounced in monolayer devices and cannot be understood in terms of known mechanisms. We propose a qualitative two-fluid vortex model in which thermal fluctuations of pinned vortices control the mobility of the free vortices. The findings provide a new perspective on fundamental questions of vortex mobility and dissipation in superconductors.

Anisotropic transport induced by DC electrical current bias near the critical current

We investigated the transport characteristics of a square shape superconducting Ta thin film under DC electrical current bias along the diagonal direction. The resistance parallel (R_∥) and perpendicular (R_⊥) to the DC current, I_DC, is measured with various magnetic fields. R_∥ and R_⊥ show contrasting dependence on I_DC. First, the critical current of R_∥ is smaller than that of R_⊥. Second, R_⊥ shows an unexpected reduction at current bias where R_∥ shows a rapid increase near the transition from a flux flow state to a normal state. The intriguing anisotropic transport characteristics can be understood by the inhomogeneous current density profile over the square sample. Diagonal DC current induces an anisotropic current density profile where the current density is high near the biasing electrode and low at the center of the sample. Accordingly, the electrical transport in the perpendicular direction could remain less affected even near the critical current of R_∥, which leads to the higher critical current in R_⊥. Complicated conduction profile may also allow the anomalous reduction in the R_⊥ before finally shifting to the normal state.

Ultra-fast kinematic vortices in mesoscopic superconductors: the effect of the self-field

Within the framework of the generalized time-dependent Ginzburg–Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The numerical simulations of the resistive state of the system show that neither material inhomogeneity nor a normal contact smaller than the sample width are required to produce an inhomogeneous current distribution inside the sample, which leads to the emergence of a kinematic vortex–antivortex pair (vortex street) solution. Further, we discuss the behaviors of the kinematic vortex velocity, the annihilation rates of the supercurrent, and the superconducting order parameters alongside the vortex street solution. We prove that these two latter points explain the characteristics of the resistive state of the system. They are the fundamental basis to describe the peak of the current–resistance characteristic curve and the location where the vortex–antivortex pair is formed.

Ultra-fast vortex motion in a direct-write Nb-C superconductor

The ultra-fast dynamics of superconducting vortices harbors rich physics generic to nonequilibrium collective systems. The phenomenon of flux-flow instability (FFI), however, prevents its exploration and sets practical limits for the use of vortices in various applications. To suppress the FFI, a superconductor should exhibit a rarely achieved combination of properties: weak volume pinning, close-to-depairing critical current, and fast heat removal from heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion at velocities of 10-15 km s-1 in a directly written Nb-C superconductor with a close-to-perfect edge barrier. The spatial evolution of the FFI is described using the edge-controlled FFI model, implying a chain of FFI nucleation points along the sample edge and their development into self-organized Josephson-like junctions (vortex rivers). In addition, our results offer insights into the applicability of widely used FFI models and suggest Nb-C to be a good candidate material for fast single-photon detectors.

SQUID-on-tip with single-electron spin sensitivity for high-field and ultra-low temperature nanomagnetic imaging

Scanning nanoscale superconducting quantum interference devices (nanoSQUIDs) are of growing interest for highly sensitive quantitative imaging of magnetic, spintronic, and transport properties of low-dimensional systems. Utilizing specifically designed grooved quartz capillaries pulled into a sharp pipette, we have fabricated the smallest SQUID-on-tip (SOT) devices with effective diameters down to 39 nm. Integration of a resistive shunt in close proximity to the pipette apex combined with self-aligned deposition of In and Sn, has resulted in SOTs with a flux noise of 42 nΦ₀ Hz^-1/2, yielding a record low spin noise of 0.29 μ_B Hz^-1/2. In addition, the new SOTs function at sub-Kelvin temperatures and in high magnetic fields of over 2.5 T. Integrating the SOTs into a scanning probe microscope allowed us to image the stray field of a single Fe₃O₄ nanocube at 300 mK. Our results show that the easy magnetization axis direction undergoes a transition from the 〈111〉 direction at room temperature to an in-plane orientation, which could be attributed to the Verwey phase transition in Fe₃O₄.

Magnetic vortex nucleation and annihilation in bi-stable ultra-small ferromagnetic particles

Vortex-mediated magnetization reversal in individual ultra-small (∼100 nm) ferromagnetic particles at low temperatures is studied by nanoSQUID magnetometry. At zero applied bias field, the flux-closure magnetic state (vortex) and the quasi uniform configuration are bi-stable. This stems from the extremely small size of the nanoparticles that lies very close to the limit of single-domain formation. The analysis of the temperature-dependent (from 0.3 to 70 K) hysteresis of the magnetization allows us to infer the nature of the ground state magnetization configuration. The latter corresponds to a vortex state as also confirmed by electron holography experiments. Based on the simultaneous analysis of the vortex nucleation and annihilation data, we estimate the magnitude of the energy barriers separating the quasi single-domain and the vortex state and their field dependence. For this purpose, we use a modified power-law scaling of the energy barriers as a function of the applied bias field. These studies are essential to test the thermal and temporal stability of flux-closure states stabilized in ultra-small ferromagnets.

Vortex lattice instability at the nanoscale in a parallel magnetic field

In superconducting materials a dynamical rearrangement of the vortex lattice occurs by forcing vortices at high velocities, until the system can become unstable. This phenomenon is known as vortex lattice instability, in which a sudden transition drives the superconducting system abruptly to the normal state. We present an experimental study on submicron bridges of NbN and NbTiN ultra-thin films with a thickness of few nanometers. The nanoscale effect on vortex lattice instability is investigated not only by the ultra-thin thickness in wide bridges, but also by changing the direction of the external magnetic field applied parallel and perpendicular to the c-axis epitaxial films. Indeed, measurements are performed for both orientations and show the vortex lattice instability, regardless of the superconducting material. Critical currents I _c as well as instability currents I* have been compared. However, only in the parallel configuration an unusual 'flying birds' feature appears in the magnetic field dependence of current switching, as a consequence of the ratio I*/I _c that is approaching 1. This amazing tendency becomes relevant for practical applications involving nanostructures, since by scaling down sample thickness and rotating the external field towards the in-plane orientation, the ultra-thin film geometry can mimic the bridge narrowing down to the nanoscale.

Use of thermal gradients for control of vortex matter in mesoscopic superconductors

Usually, the measurements of electronic and magnetic properties of superconducting samples are carried out under a constant temperature bath. On the other hand, thermal gradients induce local variation of the superconducting order parameter, and the vortex dynamics can present interesting behaviors. In this work, we solved the time-dependent Ginzburg-Landau equations simulating samples under two different thermal gradients, and considering two values of the Ginzburg-Landau parameter, [Formula: see text]. We find that both parameters, i.e. [Formula: see text] and thermal gradients, play an important role on the vortex dynamics and on the magnetization behavior of the samples.

Long-range vortex transfer in superconducting nanowires

Under high-enough values of perpendicularly-applied magnetic field and current, a type-II superconductor presents a finite resistance caused by the vortex motion driven by the Lorentz force. To recover the dissipation-free conduction state, strategies for minimizing vortex motion have been intensely studied in the last decades. However, the non-local vortex motion, arising in areas depleted of current, has been scarcely investigated despite its potential application for logic devices. Here, we propose a route to transfer vortices carried by non-local motion through long distances (up to 10 micrometers) in 50 nm-wide superconducting WC nanowires grown by Ga⁺ Focused Ion Beam Induced Deposition. A giant non-local electrical resistance of 36 Ω has been measured at 2 K in 3 μm-long nanowires, which is 40 times higher than signals reported for wider wires of other superconductors. This giant effect is accounted for by the existence of a strong edge confinement potential that hampers transversal vortex displacements, allowing the long-range coherent displacement of a single vortex row along the superconducting channel. Experimental results are in good agreement with numerical simulations of vortex dynamics based on the time-dependent Ginzburg-Landau equations. Our results pave the way for future developments on information technologies built upon single vortex manipulation in nano-superconductors.

Manipulating Multivortex States in Superconducting Structures

We demonstrate a method for manipulating small ensembles of vortices in multiply connected superconducting structures. A micron-size magnetic particle attached to the tip of a silicon cantilever is used to locally apply magnetic flux through the superconducting structure. By scanning the tip over the surface of the device and by utilizing the dynamical coupling between the vortices and the cantilever, a high-resolution spatial map of the different vortex configurations is obtained. Moving the tip to a particular location in the map stabilizes a distinct multivortex configuration. Thus, the scanning of the tip over a particular trajectory in space permits nontrivial operations to be performed, such as braiding of individual vortices within a larger vortex ensemble-a key capability required by many proposals for topological quantum computing.

Quantitative magnetic force microscopy using calibration on superconducting flux quanta

We present a new procedure that takes advantage of the magnetic flux quantization of superconducting vortices to calibrate the magnetic properties of tips for magnetic force microscopy (MFM). Indeed, a superconducting vortex, whose quantized flux is dependent upon Plank constant, speed of light and electron charge, behaves as a very well defined magnetic reference object. The proposed calibration procedure has been tested on new and worn tips and shows that the monopole point-like approximation of the probe is a reliable model. This procedure has been then applied to perform quantitative MFM experiments on a soft ferromagnetic thin film of permalloy, leading to the determination of the local out-of-plane component of the canted magnetization, together with its spatial variations across a few μm² scan area.

Scanning SQUID microscopy in a cryogen-free cooler

Scanning superconducting quantum interference device (SQUID) microscopy is a powerful tool for investigating electronic states at surfaces and interfaces by mapping their magnetic signal. SQUID operation requires cryogenic temperatures, which are typically achieved by immersing the cryostat in liquid helium. Making a transition to cryogen free systems is desirable, but has been challenging, as electric noise and vibrations are increased in such systems. We report on the successful operation of a scanning SQUID microscope in a modified Montana Instruments cryogen-free cooler with a base temperature of 4.3 K. We demonstrate scanning SQUID measurements with flux noise performance comparable to a wet system and correlate the sensor-sample vibrations to the cryocooler operation frequencies. In addition, we demonstrate successful operation in a variety of SQUID operation modes, including mapping static magnetic fields, measurement of local susceptibility, and spatial mapping of current flow distribution.

Flux flow spin Hall effect in type-II superconductors with spin-splitting field

We predict the very large spin Hall effect in type-II superconductors whose mechanism is drastically different from the previously known ones. We find that in the flux-flow regime the spin is transported by the spin-polarized Abrikosov vortices moving under the action of the Lorenz force in the direction perpendicular to the applied electric current. Due to the large vortex velocities the spin Hall angle can be of the order of unity in realistic systems based on the high-field superconductors, superconductor/ferromagnet hybrid structures or the recently developed superconductor/ferromagnetic insulator proximity structures. We propose the realization of high-frequency pure spin current generator based on the periodic structure of moving vortex lattices. We find the patterns of charge imbalance and spin accumulation generated by moving vortices, which can be used for the electrical detection of individual vortex motion. The new mechanism of inverse flux-flow spin Hall effect is found based on the driving force acting on the vortices in the presence of injected spin current which results in the generation of transverse voltage.

Microwave Radiation Detection with an Ultrathin Free-Standing Superconducting Niobium Nanohelix

We present a superconducting bolometer fabricated by a rolled-up technology that allows one to combine the two-dimensionality (2D) of the superconducting layer with a helical spiral curvature. The bolometer is formed as a free-standing Nb nanohelix acting as an ultrathin transition-edge sensor (TES) and having a negligible thermal contact to the substrate. We demonstrate the functionality of the thin-film TES by examining its microwave-detection performance in comparison with a commercial cryogenic bolometer from QMC Instruments. The nanohelix has been revealed to feature a noise equivalent power (NEP) of about 2 × 10^-10 W Hz^-1/2 at a microwave radiation power of 9 W m^-2, which is 4 orders of magnitude smaller than the NEP of the QMC sensor at a similar radiation power. Furthermore, the forecast for the nanohelix is a 1 to 2 orders of magnitude shorter response time as compared to sensors based on commonly used 1 μm thick Si₃N₄ membranes. The reason is the extremely low heat capacity of the 50 nm thick supporting material and the few contact points between the TES and the substrate. Our findings indicate that microwave radiation detection can be substantially improved by extending 2D superconducting structures into the 3D space.

Numerical Simulation of Abrikosov Vortex at Columnar Defect in Superconductor

We report a numerical modeling of single vortex depinning and its subsequent dynamics in HTS film with extended linear defects under the influence of the transport current. Numerical simulation of stable pinned vortex state and its escape from a linear defect has been performed. The non-stationary dynamics of vortex escape has been investigated and time-dependent solution for vortex displacement from the defect has been obtained. The delay effect in vortex escape process has been studied and the time delay has been estimated. The impact of processes being studied on electrodynamic properties of a superconductor has also been discussed. The dynamics of vortex escape from columnar pinning site described in the present work is important both for understanding of vortex dynamics and applying high-Tc superconductors with columnar defects.

Real-Space Probing of the Local Magnetic Response of Thin-Film Superconductors Using Single Spin Magnetometry

We report on direct, real-space imaging of the stray magnetic field above a micro-scale disc of a thin film of the high-temperature superconductor YBa₂Cu₃O7-δ (YBCO) using scanning single spin magnetometry. Our experiments yield a direct measurement of the sample's London penetration depth and allow for a quantitative reconstruction of the supercurrents flowing in the sample as a result of Meissner screening. These results show the potential of scanning single spin magnetometry for studies of the nanoscale magnetic properties of thin-film superconductors, which could be readily extended to elevated temperatures or magnetic fields.

Current-driven production of vortex-antivortex pairs in planar Josephson junction arrays and phase cracks in long-range order

Proliferation of topological defects like vortices and dislocations plays a key role in the physics of systems with long-range order, particularly, superconductivity and superfluidity in thin films, plasticity of solids, and melting of atomic monolayers. Topological defects are characterized by their topological charge reflecting fundamental symmetries and conservation laws of the system. Conservation of topological charge manifests itself in extreme stability of static topological defects because destruction of a single defect requires overcoming a huge energy barrier proportional to the system size. However, the stability of driven topological defects remains largely unexplored. Here we address this issue and investigate numerically a dynamic instability of moving vortices in planar arrays of Josephson junctions. We show that a single vortex driven by sufficiently strong current becomes unstable and destroys superconductivity by triggering a chain reaction of self-replicating vortex-antivortex pairs forming linear of branching expanding patterns. This process can be described in terms of propagating phase cracks in long-range order with far-reaching implications for dynamic systems of interacting spins and atoms hosting magnetic vortices and dislocations.

Angular dependence of vortex instability in a layered superconductor: the case study of Fe(Se,Te) material

Anisotropy effects on flux pinning and flux flow are strongly effective in cuprate as well as iron-based superconductors due to their intrinsically layered crystallographic structure. However Fe(Se,Te) thin films grown on CaF2 substrate result less anisotropic with respect to all the other iron based superconductors. We present the first study on the angular dependence of the flux flow instability, which occurs in the flux flow regime as a current driven transition to the normal state at the instability point (I*, V*) in the current-voltage characteristics. The voltage jumps are systematically investigated as a function of the temperature, the external magnetic field, and the angle between the field and the Fe(Se,Te) film. The scaling procedure based on the anisotropic Ginzburg-Landau approach is successfully applied to the observed angular dependence of the critical voltage V*. Anyway, we find out that Fe(Se,Te) represents the case study of a layered material characterized by a weak anisotropy of its static superconducting properties, but with an increased anisotropy in its vortex dynamics due to the predominant perpendicular component of the external applied magnetic field. Indeed, I* shows less sensitivity to angle variations, thus being promising for high field applications.

Josephson vortex loops in nanostructured Josephson junctions

Linked and knotted vortex loops have recently received a revival of interest. Such three-dimensional topological entities have been observed in both classical- and super-fluids, as well as in optical systems. In superconductors, they remained obscure due to their instability against collapse - unless supported by inhomogeneous magnetic field. Here we reveal a new kind of vortex matter in superconductors - the Josephson vortex loops - formed and stabilized in planar junctions or layered superconductors as a result of nontrivial cutting and recombination of Josephson vortices around the barriers for their motion. Engineering latter barriers opens broad perspectives on loop manipulation and control of other possible knotted/linked/entangled vortex topologies in nanostructured superconductors. In the context of Josephson devices proposed to date, the high-frequency excitations of the Josephson loops can be utilized in future design of powerful emitters, tunable filters and waveguides of high-frequency electromagnetic radiation, thereby pushing forward the much needed Terahertz technology.

In situ tailoring of superconducting junctions via electro-annealing

We demonstrate the in situ engineering of superconducting nanocircuitry by targeted modulation of material properties through high applied current densities. We show that the sequential repetition of such customized electro-annealing in a niobium (Nb) nanoconstriction can broadly tune the superconducting critical temperature T_c and the normal-state resistance R_n in the targeted area. Once a sizable R_n is reached, clear magneto-resistance oscillations are detected along with a Fraunhofer-like field dependence of the critical current, indicating the formation of a weak link but with further adjustable characteristics. Advanced Ginzburg-Landau simulations fully corroborate this picture, employing the detailed parametrization from the electrical characterization and high resolution electron microscope images of the region within the constriction where the material has undergone amorphization by electro-annealing.

Microfluidic manipulation of magnetic flux domains in type-I superconductors: droplet formation, fusion and fission

The magnetic flux domains in the intermediate state of type-I superconductors are known to resemble fluid droplets, and their dynamics in applied electric current is often cartooned as a "dripping faucet". Here we show, using the time-depended Ginzburg-Landau simulations, that microfluidic principles hold also for the determination of the size of the magnetic flux-droplet as a function of the applied current, as well as for the merger or splitting of those droplets in the presence of the nanoengineered obstacles for droplet motion. Differently from fluids, the flux-droplets in superconductors are quantized and dissipative objects, and their pinning/depinning, nucleation, and splitting occur in a discretized form, all traceable in the voltage measured across the sample. At larger applied currents, we demonstrate how obstacles can cause branching of laminar flux streams or their transformation into mobile droplets, as readily observed in experiments.