Phase-slip Centers Research Articles

Phase-Slip Centers as Cooling Engines

Phase-Slip Centers as Cooling Engines

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.

Phase slip from weak links formed in artificially-stacked NbSe2

The rich nature of van der Waals interactions between artificially-stacked atomic layers has been demonstrated by various quantum states and resonant tunneling transport in low-dimensional materials. However, the role of topological fluctuations in quantum transport through artificially-stacked junctions of 2D superconducting materials, and the resulting energy dissipation, remain elusive. In this research, unique phase-slip centers are designed in artificially-stacked junction areas, where nonequilibrium quasiparticles are formed and relaxed with energy dissipation. The phase slips are observed as voltage steps (peaks or valleys) in transport measurements across a junction between two exfoliated NbSe2 flakes, and at a distance of 4 μm from the junction using local and nonlocal chemical potential probes. Accordingly, two types of energy dissipation modes are newly identified in the artificially-stacked NbSe2 when subjected to an in-plane magnetic field, which implies distinct vortex formation and current flow in the superconducting junction under magnetic fields.

Hysteretic magnetoresistance in superconducting SrTiO3/LaAlO3/SrTiO3 trilayer interface system

We investigated the electrical transport properties of the SrTiO3/LaAlO3/SrTiO3 (STO/LAO/STO) trilayer interface system. We found that the trilayer exhibits superconductivity at temperatures below 0.2 K. In the superconducting regime, the magnetoresistance (MR) of the system shows pronounced hysteresis, possibly due to the interplay of ferromagnetism and superconductivity. The magnitude of MR hysteresis strongly depends on the magnetic field sweep rate, and we observed a threshold field-sweep rate below which no MR is detected. At high sweep rates, the MR exhibits superconducting-normal-superconducting transition behavior. To explain these observations, we propose a model based on the ohmic heating from superconducting phase slip centers beneath Bloch-type magnetic domain walls in the ferromagnetic layer. Furthermore, we observed complex features in the MR curves that are likely due to domain wall motion in the system.

Simulations of Dynamical Electronic Vortices in Charge and Spin Density Waves

Charge and spin density waves are typical symmetry broken states of quasi one-dimensional electronic systems. They demonstrate such common features of all incommensurate electronic crystals as a spectacular non-linear conduction by means of the collective sliding and susceptibility to the electric field. These phenomena ultimately require for emergence of static and transient topological defects: there are dislocations as space vortices and space-time vortices known as phase slip centers, i.e., a kind of instantons. Dislocations are statically built-in under a transverse electric field; their sweeping provides a conversion among the normal carriers and condensate which ensures the onset of the collective sliding. A special realization in a high magnetic field, when the density wave is driven by the Hall voltage, originated by quantized normal carriers, reveals the dynamic vorticity serving to annihilate compensating normal and collective currents. Spin density waves, with their rich multiplicative order parameter, bring to life complex objects with half-integer topologically bound vorticities in charge and spin degrees of freedom. We present the basic concepts and modelling results of the stationary states and their transient dynamics involving vorticity. The models take into account multiple fields in their mutual non-linear interactions: the complex order parameter, the self-consistent electric field, and the reaction of normal carriers. We explore the traditional time-dependent Ginzburg–Landau approach and introduce its generalization allowing the treatment of intrinsic normal carriers. The main insights and illustrations come from numerical solutions to partial differential equations for the dissipative dynamics of one and two space dimensions.

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.

Magnetic field enhanced critical current and subharmonic structures in dissipative superconducting gold nanowires

Quantum breakdown of superconductivity in low-dimensional superconducting systems has attracted enormous attention due to the underlying fluctuation. Here we report exotic phenomena observed during the current-induced breakdown of superconductivity in gold nanowires contacted by superconducting electrodes. In a 1.0 μm-long nanowire, the resistance as a function of current exhibits a random resistance switching at 1.8 K and tail-like metallic state at higher temperatures, indicating phase slips in proximity-induced superconducting nanowire. Additionally, the upper critical current is enhanced under low magnetic field, which may be attributed to the formation of spin-triplet pairing in superconducting gold nanowire. In a 1.2 μm-long gold nanowire, unexpected subharmonic structures with characteristic energy smaller than superconducting gap are superimposed on tail-like structures. The signal might be related to the axions-triggered process in phase slip center Josephson junction and thus stimulate further studies in dissipative superconducting nanowires.

Supercurrent and Phase Slips in a Ballistic Carbon Nanotube Bundle Embedded into a van der Waals Heterostructure.

We demonstrate long-range superconducting correlations in a several-micrometers-long carbon nanotube bundle encapsulated in a van der Waals stack between hBN and NbSe2. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe2 crystal as well as through the 2 μm long section not in contact with it. The large in-plane critical magnetic field of this supercurrent is an indication that even inside the carbon nanotube Cooper pairs enjoy a degree of paramagnetic protection typical of the parent Ising superconductor. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several recently proposed setups for realization of Majorana fermions in carbon nanotubes.

Phase slip center temperatures attained in superconducting NbTi filaments using an electrical pulse close to T[formula omitted

We have investigated the dynamics of dissipative states in NbTi superconducting thin films using electrical step pulse excitations on a sapphire substrate close to Tc. Excitation of a superconducting wire with a current pulse larger than the depairing critical current, Ic, gives rise to a non-equilibrium superconducting state. We identified two dissipative states, the hotspot (HS) and the phase slip center (PSC). Both are signaled by a voltage that emerges after a certain delay time td. We focused on the phase slip phenomenon in the vicinity of Tc and measured the dependence of the delay times on the value of the applied current pulse; these were fitted with the time-dependent Ginzburg-Landau (TDGL) theory due to Tinkham. The film thermal relaxation times were deduced for the phase slip center close to Tc for different samples. In addition, the temperatures at the center of the PSCs were estimated from the blackbody radiation model, and the results are consistent with the PSC formalism.

Characterization of Resistive Hotspots induced in Superconducting NbTi thin film by an electrical current pulse

We report on the creation of resistive states in NbTi superconducting filament on polished crystalline Al2O3 using the current driven pulse technique. A current pulse larger than the depairing current (Ic) initiates a dissipation in a localized spot. The non-equilibrium state described by the two dissipative mechanism pinpointed as hotspot and phase slip center. A time dependent voltage response exposes the collapse of superconductivity that occurs after a certain delay time td. We found that hotspots occur at temperatures much lower than the transition temperature. This can be clearly seen in a current versus temperature diagram. The thermal cooling and heat escape times were extracted from fitting the experimental data of the delay time to Tinkham’s amended version of the Time-Dependent Ginzburg-Landau (TDGL). The temperatures reached at the core of hotspots were determined without any parameter adjustment.

Manipulation of phase slips in carbon-nanotube-templated niobium-nitride superconducting nanowires under microwave radiation

We study the manipulation of thermal/quantum phase slips (tPSs/qPSs) in ultra-thin niobium-nitride superconducting nanowires (scNW) grown on carbon-nanotube templates. These NWs exhibit resistive steps in current–voltage (I–V) characteristics, and the number of phase slip centers (PSCs) in an NW can be tuned by the NW length. Under microwave (MW) radiation, emergence of each single PSC can be precisely controlled by varying the MW power. For thin and short scNW, a dip structure between the qPS-dominated low-temperature region and the tPS-dominated high-temperature region were observed owing to anti-proximity effect by electrodes.

Towards Understanding the Temperature and Current Sensitivities of Transition-Edge Sensors

The transition-edge sensor (TES) technology is widely applied to X-ray spectroscopy or imaging applications at wavelengths ranging from infrared to sub-mm, with the aim of potentially achieving unprecedented spectral resolution and detection sensitivity. As a critical component of the X-ray microcalorimeter, the TES affects the energy resolution via two main parameters: temperature sensitivity and current sensitivity. Tremendous efforts have been made to fabricate TESs with high temperature sensitivity and low current sensitivity, in order to enhance the energy resolution of the microcalorimeters. However, since the resistance of TESs is a complex function of temperature, current, and magnetic field, it is difficult to optimize the operational point of the detector from the first principle. We conducted an experiment to map the parameter space of a sample of MoAu TESs in the transition phase. The results show that the current sensitivity depends only on the resistance of the TESs, which is in line with the two-fluid model. The figure of merit of energy resolution dependence on the quasiparticle diffusion length has been compared with the prediction of the two-fluid model, which indicates that the time-averaging critical current of phase-slip centers is not a constant throughout the superconducting transition. The magnetic field could potentially enhance the energy resolution by reducing the charge imbalance relaxation time.

Measurement of the gap relaxation time of superconducting NbTi strips on a sapphire substrate

We report on the study of the transient voltage response of superconducting NbTi strips to an over-critical current pulse ($${I}> {I}_\mathrm{c}$$, where $${I}_\mathrm{c}$$ is the pair-breaking current). In this experiment, a localized normal spot appeared for a current amplitude larger than the critical current. The induced metastable superconducting state was identified as either a hotspot or phase-slip center. These two dissipative modes share the feature of the voltage response occurring after a delay time $${t}_\mathrm{d}$$, a solution of the time-dependent Ginzburg–Landau (TDGL) theory developed by M. Tinkham. The gap relaxation time was subsequently deduced from fitting the experimental data with the TDGL theory. An agreement was found by choosing an effective gap relaxation time $$\tau _{\Delta }= 4.75 \, \hbox {ns}$$ for a thickness of 50 nm. Assuming the proportionality to sample thickness, this indicates a thermal relaxation time of 96 ps/nm for a NbTi film sputtered at room temperature on polished crystalline $$\hbox {Al}_{{2}} \hbox {O}_{{3}}$$. If we assume that the electron and the phonon specific heats have the same ratio as for pure Nb, then it results in a phonon heat escape time $$\tau _\mathrm{es}/{d} = 32 \, \hbox {ps/nm}$$.

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.

Quasi-one-dimensional vortex matter in superconducting nanowires

It is well known that superconducting films made of a type-I material can demonstrate a type-II magnetic response, developing stable vortex configurations in a perpendicular magnetic field. Here we show that the superconducting state of a type-I nanowire undergoes more complex transformations, depending on the nanowire thickness. Sufficiently thin nanowires deviate from type I and develop multiquantum vortices and vortex clusters similar to intertype (IT) vortex states in bulk superconductors between conventional superconductivity types I and II. When the nanowire thickness decreases further, the quasi-one-dimensional vortex matter evolves towards type II so that the IT vortex configurations gradually disappear in favor of the standard Abrikosov lattice (chain) of single-quantum vortices. However, type II is not reached. Instead, an ultrathin nanowire re-enters abruptly the type-I regime while vortices tend to be suppressed by the boundaries, eventually becoming one-dimensional phase-slip centers. Our results demonstrate that arrays of nanowires can be used to construct composite superconducting materials with a widely tunable magnetic response.

The Fluctuation Formation of Phase Solitons in Superconducting Two-Band Bridges

Abstract—Based on the Ginzburg–Landau theory, the dependence of the threshold energy δFthr of formation of a phase slip center from the current for a superconducting two-band bridge has been calculated. It has been found that, in the case of sufficiently long bridges and a weak interband Josephson coupling, there is a range of currents at which fluctuation transition from the state of the zero interband phase difference to the states with a phase soliton is possible, which manifests itself in a considerable decrease in the threshold energy δFthr, and a fluctuation change in the number of phase solitons in the bridge. In the case of a strong interband coupling, no fluctuation formation of phase solitons occurs and the dependence δFthr(I) tends to the expression obtained earlier by Langer and Ambegaokar for a single-band superconductor.

From chiral anomaly to two-fluid hydrodynamics for electronic vortices

Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg–Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips – the spacetime vortices – serving for the conversion among the injected normal current and the collective one.

Emergence of Quantum Phase-Slip Behaviour in Superconducting NbN Nanowires: DC Electrical Transport and Fabrication Technologies.

Superconducting nanowires undergoing quantum phase-slips have potential for impact in electronic devices, with a high-accuracy quantum current standard among a possible toolbox of novel components. A key element of developing such technologies is to understand the requirements for, and control the production of, superconducting nanowires that undergo coherent quantum phase-slips. We present three fabrication technologies, based on using electron-beam lithography or neon focussed ion-beam lithography, for defining narrow superconducting nanowires, and have used these to create nanowires in niobium nitride with widths in the range of 20–250 nm. We present characterisation of the nanowires using DC electrical transport at temperatures down to 300 mK. We demonstrate that a range of different behaviours may be obtained in different nanowires, including bulk-like superconducting properties with critical-current features, the observation of phase-slip centres and the observation of zero conductance below a critical voltage, characteristic of coherent quantum phase-slips. We observe critical voltages up to 5 mV, an order of magnitude larger than other reports to date. The different prominence of quantum phase-slip effects in the various nanowires may be understood as arising from the differing importance of quantum fluctuations. Control of the nanowire properties will pave the way for routine fabrication of coherent quantum phase-slip nanowire devices for technology applications.

Dissipation effects in superconducting heterostructures with tungsten nanorods as weak links

Thin-film hybrid heterostructures formed by superconducting molybdenum-rhenium-alloy films with a critical temperature of about 9 K and nanoscale silicon-based semiconducting interlayers with metallic tungsten nanorods have been fabricated and studied. Current-voltage characteristics of the junctions were measured at 4.2 K and under influence of 11 GHz microwave irradiation. The evidence of a quasi-one-dimensional transport through the tungsten weak links disrupted by phase-slip centers was revealed in MoRe/doped Si/MoRe trilayers under irradiation by a high-frequency field. Also, measured current-voltage characteristics of five-layer MoRe/doped Si/MoRe/doped Si/MoRe devices exhibit a strong influence of a dissipation state in the MoRe interlayer. Namely, the switching from a superconducting state with low dissipation to a finite-conductance regime can be initiated by the emergence of an extra phase-slip center in the MoRe interlayer. Possible physical mechanisms of the two findings are discussed.

Pulse measurement of the hot spot current in a NbTiN superconducting filament

We have studied the voltage response of superconducting NbTiN filaments to a step-pulse of over-critical current I > Ic. The current induces the destruction of the Cooper pairs and initiates different mechanisms of dissipation depending on the bath temperature T. For the sample investigated, and for T above a certain T*, not far from Tc, the resistance manifests itself in the form of a phase-slip center, which turns into a normal hot spot (HS) as the step-pulse is given larger amplitudes. However, at all temperatures below T*, the destruction of superconductivity still occurs at Ic(T), but leads directly to an ever-growing HS. By lowering the current amplitude during the pulse, one can produce a steady HS and thus define a threshold HS current Ih(T). That is achieved by combining two levels of current, the first and larger one to initiate an HS, the second one to search for constant voltage response. The double diagram of the functions Ic(T) and Ih(T) was plotted in the T-range Tc/2 < T < Tc, and their crossing found at T* = (8.07 ± 0.07) K.