Retrapping Current Research Articles

Stability of thermally bistable states and their switching in superconducting weak link

Superconducting weak link (WL), acting as a Josephson junction (JJ), is one of the widely used elements in superconductor science and quantum circuits. A hysteretic JJ with robust switching between its superconducting and resistive state is an excellent candidate for single-photon detection. However, the ubiquitous fluctuations in the junction strongly influence the stability of the states and, thus, the transition from one to the other. Here, we present an experimental study of switching statistics of critical and retrapping currents of a JJ based on niobium WL in its hysteretic regime. The mean lifetimes of the two metastable states, namely, the zero-voltage superconducting state and finite-voltage resistive state, are estimated from the distributions. Further, close to the hysteresis crossover temperature, observed telegraphic noise in the time domain due to random switching between the states provides their lifetimes directly. We present a thermal model introducing a double-well (bistable) feature with an intriguing quantity with respect to the devices’ temperature states. The effects of temperature fluctuations on the stability of the states are shown. We discuss our results toward further improvement of the efficiency of superconducting WL or nanowire single-photon detectors.

Overdamped phase diffusion in hBN encapsulated graphene Josephson junctions

We investigate the zero-bias behavior of Josephson junctions made of encapsulated graphene boron nitride heterostructures in the long ballistic junction regime. For temperatures down to $2.7$ K, the junctions appear nonhysteretic with respect to the switching and retrapping currents ${I}_{C}$ and ${I}_{R}$. A small nonzero resistance is observed even around zero-bias current and scales with temperature as dictated by the phase diffusion mechanism. By varying the graphene carrier concentration we are able to confirm that the observed phase diffusion mechanism follows the trend for an overdamped Josephson junction. This is in contrast with the majority of graphene-based junctions which are underdamped and shorted by the environment at high frequencies.

Critical temperatures and critical currents of wide and narrow quasi-one-dimensional superconducting aluminum structures in zero magnetic field

We measured the critical temperatures and critical switching and retrapping currents of wide and narrow thin-film quasi-one-dimensional superconducting aluminum structures of the same thickness in zero magnetic field. For the first time, we found that the narrower the structure, the lower the critical temperature and critical current density in the structure. Probably, the influence of depairing centers that are on dirty longitudinal boundaries of the structure, is the stronger than the narrower the structure. It is found for the first time that, in most cases, the temperature-dependent switching critical current in both structures is approximated by two functions. At temperatures below the temperature corresponding to the bottom of the resistive N-S transition of structures, the switching critical current is described by the Kupriyanov–Lukichev theory. At temperatures close to the top of the N-S transition, the switching current is linear with temperature and coincides with the critical Josephson current. At these temperatures, Josephson SNS junctions are formed in structures.

On the switching current and the re-trapping current of tungsten nanowires fabricated by Focussed Ion Beam (FIB) technique

We report the superconducting properties of the tungsten (W) nanowires fabricated using focussed ion beam (FIB) technique having different wire widths of ∼120 nm and ∼290 nm. The transport properties of these wires were measured down to a temperature of 20 mK in a dilution refrigerator. We observed hysteretic current- voltage characteristics (IVCs) as a function of temperature, wherein the extend of hysteresis (difference between switching current and re-trapping current) is larger at lower temperature and diminishes near to the transition temperature. The temperature dependence of the switching current and re-trapping current were analysed using conventional models and found out to be of reasonable agreement with the models invoked. The re-trapping current agrees well with the thermal model incorporating phonon contribution in the heat dissipation process along with the electronic contribution. The equilibrium electron temperature calculated using the heat dissipation models at the critical current of the wires agrees well with respect to the transition temperature of the wire having a larger width, while for the wire of lower width, it is slightly elevated. Based on the analysis, it is believed that heat dissipation primarily because of Joule heating is the cause of the hysteretic current voltage characteristics of the nanowires.

Dynamics of Phase Switch in the Intrinsic Josephson Junctions Made of Bi2212 with Perfectly-stoichiometric Cation Compositions

We study the phase switching dynamics in the intrinsic Josephson junctions (IJJs) of Bi2Sr2CaCu2Oy (Bi2212) cuprate superconductors, focusing on the effect of stoichiometry of cation composition. The current-voltage characteristics for the IJJs with the cation composition approaching to be perfectly stoichiometric (Bi:Sr:Ca:Cu=2:2:1:2) show the highly-underdamped nature with a very small retrapping current. We found that the switching current distribution P(I) for the IJJs with perfectly stoichiometric composition and less damage had double peaks or broadened. This suggests that the phase switched junction is not always specified in the case of IJJs with stoichiometric composition, since more than one junction with almost the same switching current is associated with the observed switching events. We obtained the magnitude of a critical current density Jc and an effective temperature Tesc for the phase escape composed of a single component, by analysing the bias current dependence of the switching rate Γ(I). The results indicate that the perfectly-stoichiometric cation composition can greatly enhance the magnitude of Jc, although a crossover temperature to the macroscopic quantum tunnelling (MQT) for the higher-ordered phase switches is not influenced by the enhancement of Jc, in contrast to the conventional MQT theory.

Enhancement of superconductivity in NbN nanowires by negative electron-beam lithography with positive resist

We performed comparative experimental investigation of superconducting NbN nanowires which were prepared by means of positive- and negative electron-beam lithography with the same positive tone Poly-methyl-methacrylate (PMMA) resist. We show that nanowires with a thickness 4.9 nm and widths less than 100 nm demonstrate at 4.2 K higher critical temperature and higher density of critical and retrapping currents when they are prepared by negative lithography. Also the ratio of the experimental critical current to the depairing critical current is larger for nanowires prepared by negative lithography. We associate the observed enhancement of superconducting properties with the difference in the degree of damage that nanowire edges sustain in the lithographic process. A whole range of advantages which is offered by the negative lithography with positive PMMA resist ensures high potential of this technology for improving the performance metrics of superconducting nanowire singe-photon detectors.

Proximity-induced superconductivity in all-silicon superconductor /normal-metal junctions

We have realised laser-doped all-silicon superconducting (S)/ normal metal (N) bilayers of tunable thickness and dopant concentration. We observed a strong reduction of the bilayers critical temperature when increasing the normal metal thickness, a signature of the highly transparent S/N interface associated to the epitaxial sharp laser doping profile. We extracted the interface resistance by fitting with the linearised Usadel equations, demonstrating a reduction of one order of magnitude from previous superconductor/doped Si interfaces. In this well controlled crystalline system we exploited the low resistance S/N interfaces to elaborate all-silicon lateral SNS Josephson junctions with long range proximity effect. Their dc transport properties, such as the critical and retrapping currents, could be well understood in the diffusive regime. Furthermore, this work lead to the estimation of important parameters in ultra-doped superconducting Si, such as the Fermi velocity, the coherence length, or the electron-phonon coupling constant, fundamental to conceive an all-silicon superconducting electronics.

Micron size superconducting quantum interference devices of lead (Pb)

Micron size superconducting quantum interference devices (μ-SQUID) of lead (Pb), for probing nano-magnetism, were fabricated and characterized. In order to get continuous Pb films with small grain size, Pb was thermally evaporated on a liquid nitrogen cooled Si substrate. Pb was sandwiched between two thin Cr layers for improved adhesion and protection. The SQUID pattern was made by e-beam lithography with Pb lift-off after deposition. The current–voltage characteristics of these devices show a critical current, which exhibits the expected SQUID oscillations with magnetic field, and two re-trapping currents. As a result these devices have hysteresis at low temperatures, which disappears just below the critical temperature.

Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Fluxon transmission through impurities of different shape in a quasi-one-dimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length λJ or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several λJ) junction width is observed.

Dynamics of superconducting nanowires shunted with an external resistor

We present the first study of superconducting nanowires shunted with an external resistor, geared towards understanding and controlling coherence and dissipation in nanowires. The dynamics is probed by measuring the evolution of the V-I characteristics and the distributions of switching and retrapping currents upon varying the shunt resistor and temperature. Theoretical analysis of the experiments indicates that as the value of the shunt resistance is decreased, the dynamics turns more coherent presumably due to stabilization of phase-slip centers in the wire and furthermore the switching current approaches the Bardeen's prediction for equilibrium depairing current. By a detailed comparison between theory and experimental, we make headway into identifying regimes in which the quasi-one-dimensional wire can effectively be described by a zero-dimensional circuit model analogous to the RCSJ (resistively and capacitively shunted Josephson junction) model of Stewart and McCumber. Besides its fundamental significance, our study has implications for a range of promising technological applications.

Enhancement of the retrapping current of superconducting microbridges of finite length

We theoretically find that the resistance of a superconducting microbridge/nanowire {\it decreases} while the retrapping current $I_r$ for the transition to the superconducting state {\it increases} when one suppresses the magnitude of the order parameter $|\Delta|$ in the attached superconducting leads. This effect is a consequence of the increased energy interval for diffusion of the 'hot' nonequilibrium quasiparticles (induced by the oscillations of $|\Delta|$ in the center of the microbridge) to the leads. The effect is absent in short microbridges (with length less than the coherence length) and it is relatively weak in long microbridges (with length larger than the inelastic relaxation length of the nonequilibrium distribution function). A nonmonotonous dependence of $I_r$ on the length of the microbridge is predicted. Our results are important for the explanation of the enhancement of the critical current and the appearance of negative magnetoresistance observed in many recent experiments on superconducting microbridges/nanowires.

Retrapping current, self-heating, and hysteretic current-voltage characteristics in ultranarrow superconducting aluminum nanowires

Hysteretic I-V (current-voltage) is studied in narrow Al nanowires. The nanowires have a cross section as small as 50 nm^2. We focus on the retapping current in a down-sweep of the current, at which a nanowire re-enters the superconducting state from a normal state. The retrapping current is found to be significantly smaller than the switching current at which the nanowire switches into the normal state from a superconducting state during a current up-sweep. For wires of different lengths, we analyze the heat removal due to various processes, including electronic and phonon processes. For a short wires 1.5 um in length, electronic thermal conduction is effective; for longer wires 10um in length, phonon conduction becomes important. We demonstrate that the measured retrapping current as a function of temperature can be quantitatively accounted for by the selfheating occurring in the normal portions of the nanowires to better than 20 % accuracy. For the phonon processes, the extracted thermal conduction parameters support the notion of a reduced phase-space below 3-dimensions, consistent with the phonon thermal wavelength having exceeded the lateral dimensions at temperatures below ~ 1.3K. Nevertheless, surprisingly the best fit was achieved with a functional form corresponding to 3-dimensional phonons, albeit requiring parameters far exceeding known values in the literature.

Macroscopic Superconducting Current through a Silicon Surface Reconstruction with Indium Adatoms:Si(111)−(7×3)−In

Macroscopic and robust supercurrents are observed by direct electron transport measurements on a silicon surface reconstruction with In adatoms [Si(111)-(√7 × √3)-In]. The superconducting transition manifests itself as an emergence of the zero resistance state below 2.8 K. I-V characteristics exhibit sharp and hysteretic switching between superconducting and normal states with well-defined critical and retrapping currents. The two-dimensional (2D) critical current density J(2D,c) is estimated to be as high as 1.8 A/m at 1.8 K. The temperature dependence of J(2D,c) indicates that the surface atomic steps play the role of strongly coupled Josephson junctions.

Microwave power dependence of the retrapping current of superconducting nanostrips

The microwave power density absorbed in the normal state by continuously irradiated superconducting Nb and NbN nanostrips is extracted from their electrical transport properties. The procedure is based on the reduction of the retrapping current (i.e., the minimum applied current required to sustain a dissipative region inside a superconducting microbridge) that results from the microwave dissipation. The power effectively absorbed by the nanostrips varies linearly with the input power level and falls in the μWμm–3 range. At a given microwave frequency, the relation between the input power and the absorbed power does not depend on the coolant temperature. In addition, the upper limit of the detection range is given by the heat removal capabilities through the substrate. When the absorbed microwave power exceeds this temperature-dependent heat removal threshold, normal hotspot domains are stabilized down to zero bias current. The determination of the microwave power absorbed by superconducting samples in the normal state may be of practical interest in the field of incident power detection.

Evidence for Two Time Scales in Long SNS Junctions

We use microwave excitation to elucidate the dynamics of long superconductor-normal metal-superconductor Josephson junctions. By varying the excitation frequency in the range 10 MHz-40 GHz, we observe that the critical and retrapping currents, deduced from the dc voltage versus dc current characteristics of the junction, are set by two different time scales. The critical current increases when the ac frequency is larger than the inverse diffusion time in the normal metal, whereas the retrapping current is strongly modified when the excitation frequency is above the electron-phonon rate in the normal metal. Therefore the critical and retrapping currents are associated with elastic and inelastic scattering, respectively.

Effect of quasi-particle injection on retrapping current of Josephson junction

We report that the energy dissipation of Josephson junction can be controlled by quasi-particle injection. We fabricated two Josephson junctions on the narrow aluminum wire and controlled the energy dissipation of one junction by quasi-particle injection from the other. We observed the retrapping current increased as the quasi-particles were injected. We also studied the heating effect of our measurement.

Critical currents of strongly disordered ultra-thin superconducting films

Quench-condensed films of various metals are well known systems for studying the superconducting state in presence of strong disorder. Critical currents of superconducting films of Bi and Sn with sheet resistance <500 Ω were found to vary with temperature according to the relation I c( T)= I c(0)(1−( T/ T c) 4). The result was found to be independent of the substrate used. The observed dependence implies a variation of the superconducting gap Δ( T)∼(1−( T/ T c) 4) 1/2, near T c. This is different from the behaviour of a BCS type gap near T c but consistent with some existing measurements on fabricated 2-D Josephson junction arrays. The I– V characteristics of these films also show hysteresis, indicating the presence of underdamped intergrain Josephson coupling. The values of the intergrain resistances and capacitances are estimated from the ratios of the observed retrapping and critical currents.

π-phase jump of magnetic-field dependence of retrapping current in dc SQUID’s

We measured the retrapping current of a small-capacitance underdamped dc superconducting quantum interference device (SQUID) at low temperatures as a function of magnetic field. We found that the relative phase relation between the magnetic-field dependence of the retrapping current and that of the switching current jumped from 0 to $\ensuremath{\pi}$ at ${E}_{\mathrm{J}}\ensuremath{\sim}{E}_{\mathrm{C}},$ where ${E}_{\mathrm{J}}$ and ${E}_{\mathrm{C}}$ are the Josephson energy and the charging energy of a Cooper pair. This phenomenon cannot be reproduced by a model that approximates the SQUID as a single junction with a controllable switching current. It can be explained phenomenologically by taking into account two kinds of dissipation that arise from ac currents flowing through the lead and along the SQUID's loop.

Observation of Qubit State with a dc-SQUID and Dissipation Effect in the SQUID

Two states of a flux qubit with three Josephson junctions were shown in a single measurement with a dc-SQUID. The qubit is an aluminum superconductor loop surrounded by a dc-SQUID for readout. It has two states, which have persistent currents flowing in opposite directions. The readout data for three samples with different junction sizes suggest that the probability distribution for the double-well potential depends on the ratio of EJ/EC, where EJ is the Josephson energy and EC is the charging energy. The probability distribution was estimated by calculating the wavefunctions and energy levels for the measured samples. We measured the retrapping current of a dc-SQUID without the qubit as a function of the magnetic field. It was found that the relative phase relation for the magnetic field dependence of the retrapping current jumped from 0 to π at EJ ≈ EC. This jump can be explained phenomenologically by taking into account the two kinds of dissipation arising from ac currents flowing through the lead and along the SQUID loop. The fact that the jump occurred at EJ ≈ EC strongly suggests that the quantum nature of the electromagnetic environment needs to be taken into account in order to understand the origin of the dissipation.

Transport properties of superconducting YBa 2Cu 3O 7− δ nanobridges prepared by wet-chemical etching

Superconducting YBa 2Cu 3O 7− δ -nanobridges with lateral dimensions between 60 and 200 nm have been patterned by a self-limiting wet-chemical etching process. Optimally doped bridges show transition temperatures of 85–87 K. The current–voltage ( IV) characteristics exhibit flux-flow transport properties with voltage jumps appearing at higher current densities I ∗ . At lower temperatures, the IV-characteristics become hysteretic. Although the temperature dependence of the retrapping current can be described by the hot-spot model, a thermal effect as origin of the voltage jump can be excluded since I ∗(T)∝(1−T/T c ) and the dissipated power P ∗=U ∗×I ∗ increases with increasing T. Instead, a flux-flow instability as has previously been observed in wide bridges is proposed. Both, v ∗(B) and τ in are extracted from the data.