Phase-slip Lines Research Articles

Some aspects of the resistive-to-normal state transition caused by direct and microwave currents in superconducting thin films with phase slip lines

Based on analysis of current-voltage characteristics and imaging of the resistive state of thin-film tin strips using low-temperature laser scanning microscopy (LTLSM), the process of destruction of superconductivity by current and microwave irradiation with the formation and spatial rearrangement of the order parameter phase slip lines, and their transformation into discrete localized normal domains are shown. The prospects of LTLSM are considered from the point of view of the study of the high-frequency properties of superconducting structures and spatial characteristics in the pre-critical state for instrumental applications.

Roundabout-like defect as a guide of phase-slip lines in a superconducting thin film at low temperature

AbstractIn this work, we examined the kinematic vortex state in a low-temperature, mesoscopic superconducting thin film in presence of an external applied current $$\varvec{J}$$ J , at zero magnetic field. We analyzed the voltage-current ($$\varvec{V-I}$$ V - I ), resistivity-current ($$\varvec{R-I}$$ R - I ) curves, as well as the vortex-anti-vortex velocity $$\varvec{V_m}$$ V m and the superconducting-electron density (norm of the superconduting order parameter $$\varvec{\psi }$$ ψ ) as an applied current function. Additionally, we have calculated the voltage as a function of characteristic time ($$\varvec{V-t}$$ V - t ). The sample presents a roundabout shaped pinning center fabricated with a lower low-temperature superconducting material, which allows for control over the vortex dynamics within the sample. To study this system, we have solved the generalized time-dependent Ginzburg-Landau equations for a single-condensate system. Our results demonstrate that the kinematic vortices enter the sample through regions where the superconductivity is depleted, revealing an intriguing and novel behavior of the phase-slip lines in the defect. We found that when a higher $$\varvec{J}$$ J is applied and the defect is not centered, the point where the vortex anti-vortex pairs enter the film moves away from the defect and are located in a point tangent to the outer circle of the defect. Besides, our results show a way to control the dynamics of the vortices, critical currents, and points of annihilation or creation of the cinematic vortices by including defects in the sample, important in the design and development of devices applied in industry and engineering.

Phase-Slip Lines and Anomalous Josephson Effects in Tungsten Nanoscale Cluster-Based Topological Insulator Nanobridges: Implications for Topologically Protected Qubits and Quantum Sensors

Phase-Slip Lines and Anomalous Josephson Effects in Tungsten Nanoscale Cluster-Based Topological Insulator Nanobridges: Implications for Topologically Protected Qubits and Quantum Sensors

Current–voltage characteristics of focused ion beam fabricated superconducting tungsten meanders

We report on the superconducting properties and intermediate resistive steps (IRS) observed in the current–voltage characteristics (IVC) of tungsten meander (MW) structures fabricated using focused ion beam (FIB) technique. Three number of MWs were studied with individual wire widths of 240 nm, 640 nm and 850 nm with superconducting transition temperatures () of 4.5 K, 4.55 K and 4.60 K respectively. The measured normal state resistance values at 8 K for these wires are of ∼182 kΩ, ∼49 kΩ and ∼32 kΩ, respectively as a function of increasing wire widths; are higher than the quantum of resistance ( is a Planck constant and is electronic charge) indicating extreme disorder nature of the fabricated samples. The variation of resistance with respect to temperature (for ) follows the theoretical simulation of weak-link induced thermally activated phase slip (WL-TAPS) for the MW wire of width ∼240 nm, while for other samples the convergence between WL-TAPS and the experimental data are not so satisfactory. Though the IRS features are present in all the samples with varying degree of prominence, an external magnetic field causes its evolution demarcating different boundary lines with respect to temperatures. Herein, we believe that the occurrence of IRS is due to phase slip (PS) mechanism which further proliferates through phase slip centers or phase slip lines in IVC either with respect to temperature or magnetic field. As per our knowledge, such IRS features are not being reported for W-meander wires fabricated using FIB technique. The observation of PS (IRS) features is promising for the use of FIB fabricated W nanowires for various quantum applications including single photon detector, bolometers.

Memristor-like behavior and negative resistance in a superconductor/insulator/ferromagnet device with a pinholes-governed interface

We investigate the voltage–current characteristics of a superconductor–insulator–ferromagnet heterostructure, where the insulating layer contains pinhole-defects. The superconducting layer exhibits multiple voltage jumps that are hysteretic with the current sweep direction. This characteristic of the resistive state is due to pinholes that induce local, distinct, coupling regions between the superconducting and ferromagnetic layers which may generate phase-slip lines or vortex channeling. These findings point to a magnetically driven design of a superconductor memristor. Concomitantly, the junctions display both absolute and differential negative resistances below the superconducting critical temperature and current. This anomalous behavior is analyzed using a circuit approach and is attributed to current passing through pinholes within the insulating layer. These two unique effects, which stem from the special topology of the pinholes-governed interface can be applied in superconductor-based switches and memory devices.

Superconducting source and sensor of single bubbles to study nucleate boiling of liquid helium

Joule heat generated by resistive elements of cryogenic micro- and nanodevices often originates boiling of the cooling cryogenic liquids (helium, nitrogen). The article proposes an experimental method to explore the dynamics of the formation and development of a single vapor bubble in cryogenic liquid by sensing the temperature change of a superconducting thin-film microbridge being in the resistive state with single phase slip center or line. It serves both the source of heat for generating single bubbles and the surface temperature sensor due to its temperature-dependent excess current. The average bubble detachment rate and the average single bubble volume were experimentally determined for nucleate helium boiling. The obtained values are in good agreement with the data of other authors found in literature.

Dynamical vortex phase diagram of two-dimensional superconductivity in gated MoS2

Recent discoveries of two-dimensional (2D) superconductors have uncovered various new aspects of physical properties including vortex matter. In this paper, we report transport properties and a dynamical phase diagram at zero magnetic field in ion-gated MoS2. In addition to the universal jump in the current-voltage characteristic showing unambiguous evidence of the Berezinskii-Kosterlitz-Thouless (BKT) transition, we observed multiple peaks in the temperature- and current-derivative of the electrical resistance, based on which a dynamical phase diagram in the current-temperature plane was constructed. We found current-induced dynamical states of vortex-antivortex pairs, containing that with the phase slip line. Also, we present a global phase diagram of vortices in gated MoS2 which captures the nature of vortex matter of clean 2D superconductors.

Length dependence of the number of phase slip lines in a superconducting strip

We study the superconducting state of a strip under an transport current Ja and an external magnetic field H. We show that the value of the critical currents at which the vortex–antivortex (V–Av) pair penetrates the sample, the number of phase-slip lines, and their average velocities and dynamics strongly depend on the size of the sample L. Our investigation was carried out by numerically solving the two-dimensional generalized time-dependent Ginzburg–Landau equations (GTDGL).

Effect of meter-range electromagnetic irradiation on the current-voltage characteristics of wide superconducting films

The effect of the electromagnetic irradiation on the current-voltage characteristics (IVCs) of a wide superconducting film is experimentally investigated. In contrast to the microwave field (several GHz) which suppresses vortex resistivity, the action of the rf field (tens of MHz) leads to significant expansion of the linear part of the IVC due to rapid suppression of the critical current with a slower change in the upper stability limit of the vortex state where the phase-slip lines (PSLs) occur. With an increase in the rf power, the stepwise structure of the IVC associated with the PSLs becomes smoothed and eventually disappears. A model of the IVC in the adiabatic regime is proposed, which explains the effects of smoothing of the voltage steps and the suppression of the critical current.

Use of Transition Models to Design High Performance TESs for the LCLS-II Soft X-Ray Spectrometer.

We are designing an array of transition-edge sensor (TES) microcalorimeters for a soft X-ray spectrometer at the Linac Coherent Light Source at SLAC National Accelerator Laboratory to coincide with upgrades to the free electron laser facility. The complete spectrometer will have 1000 TES pixels with energy resolution of 0.5 eV full-width at half-maximum (FWHM) for incident energies below 1 keV while maintaining pulse decay-time constants shorter than 100 μs. Historically, TES pixels have often been designed for a particular scientific application via a combination of simple scaling relations and trial-and-error experimentation with device geometry. We have improved upon this process by using our understanding of transition physics to guide TES design. Using the two-fluid approximation of the phase-slip line model for TES resistance, we determine how the geometry and critical temperature of a TES will affect the shape of the transition. We have used these techniques to design sensors with a critical temperature of 55 mK. The best sensors achieve an energy resolution of 0.75 eV FWHM at 1.25 keV. Building upon this result, we show how the next generation of sensors can be designed to reach our goal of 0.5 eV resolution.

Substrate mediated nitridation of niobium into superconducting Nb2N thin films for phase slip study

Here we report a novel nitridation technique for transforming niobium into hexagonal Nb2N which appears to be superconducting below 1K. The nitridation is achieved by high temperature annealing of Nb films grown on Si3N4/Si (100) substrate under high vacuum. The structural characterization directs the formation of a majority Nb2N phase while the morphology shows granular nature of the films. The temperature dependent resistance measurements reveal a wide metal-to-superconductor transition featuring two distinct transition regions. The region close to the normal state varies strongly with the film thickness, whereas, the second region in the vicinity of the superconducting state remains almost unaltered but exhibiting resistive tailing. The current-voltage characteristics also display wide transition embedded with intermediate resistive states originated by phase slip lines. The transition width in current and the number of resistive steps depend on film thickness and they both increase with decrease in thickness. The broadening in transition width is explained by progressive establishment of superconductivity through proximity coupled superconducting nano-grains while finite size effects and quantum fluctuation may lead to the resistive tailing. Finally, by comparing with Nb control samples, we emphasize that Nb2N offers unconventional superconductivity with promises in the field of phase slip based device applications.

Phase-Slip Lines in Wide Superconducting Strips: Charge and Spin Relaxation Lengths

Penetration of spin-polarized charges from a nearby ferromagnetic metallic layer into 100-μm-wide superconducting films of Pb and Mo–Re alloy with similar critical parameters but quite different spin-orbit coupling strengths is studied. It is shown that the diffusion of magnetic properties into a nearby superconductor can be employed as an electrically tunable source of phase-slip events manifesting itself by a staircase response in current-voltage characteristics of the superconductor with discrete metastable resistivity states. Unlike for normal metals, the spin injection into an adjoining quasi-two-dimensional superconducting strip creates not only spin but also charge imbalance in the quasiparticle population which are not necessarily relaxing over the same time scale. Interplay of the two intrinsic length scales sets the width of a phase-slip line in superconducting strips under the injection which may change from nano- to micro-scales. Its experimental determination can be used for estimating the longest relaxation length in a superconductor. Our observations show that spin-orbit coupling in superconductors may lead to novel non-trivial effects linking spin and charge degrees of freedom.

Phase slip lines in superconducting few-layer NbSe2 crystals

We show the results of two-terminal and four-terminal transport measurements on few-layer NbSe2 devices at large current bias. In all the samples measured, transport characteristics at high bias are dominated by a series of resistance jumps due to nucleation of phase slip lines, the two dimensional analogue of phase slip centers. In point contact devices the relatively simple and homogeneous geometry enables a quantitative comparison with the model of Skocpol, Beasley and Tinkham. In extended crystals the nucleation of a single phase slip line can be induced by mechanical stress of a region whose width is comparable to the charge imbalance equilibration length.

Experimental evidence for hotspot and phase-slip mechanisms of voltage switching in ultrathin YBa2Cu3O7–x nanowires

We have fabricated ultrathin $\mathrm{YB}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{7--x}$ nanowires with a high critical current density and studied their voltage switching behavior in the 4.2--90 K temperature range. A comparison of our experimental data with theoretical models indicates that, depending on the temperature and nanowire cross section, voltage switching originates from two different mechanisms: hotspot-assisted suppression of the edge barrier by the transport current and the appearance of phase-slip lines in the nanowire. Our observation of hotspot-assisted voltage switching is in good quantitative agreement with predictions based on the Aslamazov-Larkin model for an edge barrier in a wide superconducting bridge.

Effect of pinning on the vortex motion in superconducting strip

We study the effect of different sizes and shapes of pinning centers on the vortex motion in superconducting strip in the presence of external current and magnetic field using the time-dependent Ginzburg–Landau theory. The size of pinning centers obviously affects the threshold current corresponding to the appearance of phase-slip line. The larger size results in a considerable decrease of the threshold current and a larger output voltage. For the same size, the different shapes of pinning centers lead to different behaviors of vortices. The dynamic behavior of vortices is dependent on the minimum distance dm between pinning center and the sample surface and the maximum length lm of the pinning center paralleling with the sample edge. However, the obvious changes are observed in the dynamic of vortex motion in superconductor with different pinning centers.

Phase-Slip Events in a Wide Superconducting Film Induced by Proximity to a Half-Metallic Strip

Emergence of phase-slip lines is one of the main mechanisms for dissipation in current-carrying superconducting thin films with lateral dimensions larger than the superconducting coherence length. We show that effective control of the wide resistive region between dissipation-free and completely ohmic transport regime can be achieved by evaporating a half-metallic strip, made from a Co2CrAl compound in our case, directly onto a type-II superconducting film, a Mo56Re44 alloy in our case, and tuning the spin-polarized injection current. We have revealed steps-like features in current–voltage characteristics of the Mo–Re films, even without any injection, and explained it within a “self-injection” scenario in contacts formed by ferromagnetic (F) and superconducting (S) layers. At certain injection levels, a set of resistive metastable states following the main criteria for the phase-slip events was observed. We have found that low magnetic fields, even less than the lower critical field of the Mo–Re alloy, have a significant impact on the resistive transition region of the S film probably due to their effect on the magnetic ordering in the F strip, thus producing a strong coupling between transport characteristics of proximized S and F layers.

Dynamics of vortex–antivortex pair in a superconducting thin strip with narrow slits**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant Nos. 310812171011 and G2016KY0305), the National Natural Science Foundation of China (Grant No. 11421062), and the National Key Project of Magneto-Constrained Fusion Energy Development Program, China (Grant No. 2013GB110002).

In the framework of phenomenological time-dependent Ginzburg–Landau (TDGL) formalism, the dynamical properties of vortex–antivortex (V-Av) pair in a superconductor film with a narrow slit was studied. The slit position and length can have a great impact not only on the vortex dynamical behavior but also the current–voltage (I–V) characteristics of the sample. Kinematic vortex lines can be predominated by the location of the slit. In the range of relatively low applied currents for a constant weak magnetic field, kinematic vortex line appears at right or left side of the slit by turns periodically. We found such single-side kinematic vortex line cannot lead to a jump in the I–V curve. At higher applied currents the phase-slip lines can be observed at left and right sides of the slit simultaneously. The competition between the vortex created at the lateral edge of the sample and the V-Av pair in the slit will result in three distinctly different scenarios of vortex dynamics depending on slit length: the lateral vortex penetrates the sample to annihilate the antivortex in the slit; the V-Av pair in the slit are driven off and expelled laterally; both the lateral vortex and the slit antivortex are depinned and driven together to annihilation in the halfway.

The guidance of kinematic vortices in a mesoscopic superconducting strip with artificial defects

Within the time-dependent Ginzburg–Landau (TDGL) theory, we theoretically investigated the dynamic properties of vortex–antivortex (V–Av) pairs in a current-carrying superconductor strip with one tilted slit or two transversely/longtitudinally arranged slits in the presence of a weak magnetic field. The effect of the rotation angle on the resistive state in the sample with one tilted slit was considered. The location of phase slippage in the sample can be predetermined by the rotation angle of the tilted slit. We found the coalescence of the phase-slip lines (PSLs) during a periodic multiharmonic voltage oscillation. This leads to two stages of voltage oscillation at zero applied field and three stages at weak magnetic field since the coalescence of left and right PSLs are staggered in the latter case. Moreover, the influence of relative position and size of the two slits on the transport properties of the sample are also studied. The dynamic behavior of V–Av pairs depends on not only the slit length but also their horizontal or vertical interval distance between the two slits. Since the geometry of sample has an important influence on the distribution of supercurrent across the sample, we demonstrate the possibility to efficiently guide the kinematic vortices by adjusting the relevant parameters.

Onset, evolution, and magnetic braking of vortex lattice instabilities in nanostructured superconducting films

In 1976 Larkin and Ovchinnikov [Sov. Phys. JETP 41, 960 (1976)] predicted that vortex matter in superconductors driven by an electrical current can undergo an abrupt dynamic transition from a flux-flow regime to a more dissipative state at sufficiently high vortex velocities. Typically this transition manifests itself as a large voltage jump at a particular current density, so-called instability current density $J^*$, which is smaller than the depairing current. By tuning the effective pinning strength in Al films, using an artificial periodic pinning array of triangular holes, we show that a unique and well defined instability current density exists if the pinning is strong, whereas a series of multiple voltage transitions appear in the relatively weaker pinning regime. This behavior is consistent with time-dependent Ginzburg-Landau simulations, where the multiple-step transition can be unambiguously attributed to the progressive development of vortex chains and subsequently phase-slip lines. In addition, we explore experimentally the magnetic braking effects, caused by a thick Cu layer deposited on top of the superconductor, on the instabilities and the vortex ratchet effect

Resistive states in wide superconducting films induced by dc and ac currents (Review Article)

This review is devoted to the studies of the resistive state in wide superconducting films induced by dc and ac currents in the absence of an external magnetic field. It is found experimentally that the current-voltage characteristics and their parameters are well described by the Aslamazov–Lempitskii theory of the resistive vortex state, which has long been lacking an adequate evidence to support it. There is experimental evidence that the vortex mechanism of resistivity is absent for currents exceeding the maximum current at which the resistive vortex state exists in wide films. The non-vortex nature of phase slip lines (PSL) in wide films is proved experimentally. It is shown that the phase-slip lines arise in a wide superconducting film subjected to an external microwave irradiation with the power exceeding some critical value. The resistance of these phase-slip lines depends on irradiation frequency. Results obtained in studies of PSL in wide films are similar to those obtained for the phase-slip centers in narrow channels. This suggests the identical nature of the phase-slip processes in these two phenomena. It is established that the current-carrying resistive state of a wide film arises due to two different mechanisms that occur one after the other: the penetration into the film and transverse motion of the Pearl vortices induced by the magnetic field of the transport current and the emergence of the phase-slip lines of the superconducting order parameter.