Weak-link Josephson Junctions Research Articles

Magnetic, Thermal, and Topographic Imaging with a Nanometer-Scale SQUID-On-Lever Scanning Probe

Scanning superconducting quantum interference device (SQUID) microscopy is a magnetic imaging technique combining high-field sensitivity with nanometer-scale spatial resolution. State-of-the-art SQUID-on-tip probes are now playing an important role in mapping correlation phenomena, such as superconductivity and magnetism, which have recently been observed in two-dimensional van der Waals materials. Here, we demonstrate a scanning probe that combines the magnetic and thermal imaging provided by an on-tip SQUID with the tip-sample distance control and topographic contrast of a non-contact atomic force microscope (AFM). We pattern the nanometer-scale SQUID, including its weak-link Josephson junctions, via focused ion beam milling at the apex of a cantilever coated with Nb, yielding a sensor with an effective diameter of 365 nm, field sensitivity of 9.5 $\text{nT}/\sqrt{\text{Hz}}$ and thermal sensitivity of 620 $\text{nK}/\sqrt{\text{Hz}}$, operating in magnetic fields up to 1.0 T. The resulting SQUID-on-lever is a robust AFM-like scanning probe that expands the reach of sensitive nanometer-scale magnetic and thermal imaging beyond what is currently possible.

The discovery, disappearance and re-emergence of radiation-stimulated superconductivity

We trace the historical fate of experiment and theory of microwave-stimulated superconductivity as originally reported for constriction-type superconducting weak links. It is shown that the observed effect disappeared by improving weak links to obtain the desired Josephson properties. Separate experiments were carried out to evaluate the validity of the proposed theory of Eliash’berg for energy-gap-enhancement in superconducting films in a microwave field, without reaching a full quantitatively reliable measurement of the stimulated energy gap in a microwave field, but convincing enough to understand the earlier deviations from the Josephson-effect. Over the same time period microwave-stimulated superconductivity continued to be present in superconductor-normal metal-superconductor Josephson weak links. This experimental body of work was left unexplained for several decades and could only be understood properly after the microscopic theory of the proximity-effect had matured enough, including its non-equilibrium aspects. It implies that the increase in critical current in weak-link Josephson-junctions is due to an enhancement of the phase-coherence rather than to an enhancement of the energy-gap as proposed by Eliash’berg. The complex interplay between proximity-effect and the occupation of states continues to be, in a variety of ways, at the core of the ongoing research on hybrid Josephson-junctions. The subject of radiation-enhanced superconductivity has re-emerged in the study of the power-dependence of superconducting microwave resonators, but also in the light-induced emergence of superconductivity in complex materials.

Theory of a weak-link superconductor-ferromagnet Josephson structure

We propose a model for the theoretical description of a weak-link Josephson junction, in which the weak link is spin-polarized due to proximity to a ferromagnetic metal (S-(F|S)-S). Employing Usadel transport theory appropriate for diffusive systems, we show that the weak link is described within the framework of Andreev circuit theory by an effective self-energy resulting from the implementation of spin-dependent boundary conditions. This leads to a considerable simplification of the model, and allows for an efficient numerical treatment. As an application of our model, we show numerical calculations of important physical observables such as the local density of states, proximity-induced minigaps, spin-magnetization, and the phase and temperature-dependence of Josephson currents of the S-(F|S)-S system. We discuss multi-valued current-phase relationships at low temperatures as well as their crossover to sinusoidal form at high temperatures. Additionally, we numerically treat (S-F-S) systems that exhibit a magnetic domain wall in the F region and calculate the temperature- dependence of the critical currents.

Nanoscale nonlinear radio frequency properties of bulk Nb: Origins of extrinsic nonlinear effects

The performance of Niobium-based Superconducting Radio Frequency (SRF) particle accelerator cavities can be sensitive to localized defects that give rise to quenches at high accelerating gradients. In order to identify these material defects on bulk Nb surfaces at their operating frequency and temperature, a wide bandwidth microwave microscope with localized and strong RF magnetic fields is developed by integrating a magnetic write head into the near-field microwave microscope to enable mapping of the local electrodynamic response in the multi-GHz frequency regime at cryogenic temperatures. This magnetic writer demonstrates a localized and strong RF magnetic field on bulk Nb surface with $B_{surface}$ > 102 mT and sub-micron resolution. By measuring the nonlinear response of the superconductor, nonlinearity coming from the nano-scale weak link Josephson junctions due to the contaminated surface in the cavity fabrication process is demonstrated.

Characteristics of YBa2Cu3O7−x/SrTiO3/YBa2Cu3O7−x films formed by chemical solution deposition

From the perspective of practical application, chemical solution deposition (CSD) technology is promising for the preparation of superconductor/insulator/superconductor (SIS) junctions with YBa2Cu3O7−x films as the superconducting layers compared with the various vacuum deposition processes currently used. In this study, trilayer films of YBa2Cu3O7−x/SrTiO3/YBa2Cu3O7−x were prepared using the CSD method. It was observed that when the nominal thickness of the interlayer (SrTiO3) was 14nm, the I–V curve of the structure was similar to that of a weak-link Josephson junction due to the predominant weak links of microbridges and point contacts. When the nominal thickness of the interlayer was 40nm, the I–V curve exhibited hysteresis due to the predominant tunnel effect. When the nominal thickness of the interlayer was 120nm, the various weak links for superconducting coupling were absent, and the resistivity between the two YBa2Cu3O7−x layers was 3.4×107Ωcm, which can satisfy the requirements for isolating electrodes in superconducting electron devices.

A dispersive nanoSQUID magnetometer for ultra-low noise, high bandwidth flux detection

We describe a dispersive nanoSQUID (nanoscale superconducting quantum interference device) magnetometer comprised of two variable thickness aluminum weak-link Josephson junctions shunted in parallel with an on-chip capacitor. This arrangement forms a nonlinear oscillator with a tunable 4–8 GHz resonant frequency with a quality factor Q = 30 when coupled directly to a 50 Ω transmission line. In the presence of a near-resonant microwave carrier signal, a low frequency flux input generates sidebands that are readily detected using microwave reflectometry. If the carrier excitation is sufficiently strong, then the magnetometer also exhibits parametric gain, resulting in a minimum effective flux noise of 30 nΦ0 Hz−1/2 with 20 MHz of instantaneous bandwidth. If the magnetometer is followed with a near-quantum-noise-limited Josephson parametric amplifier, we can increase the bandwidth to 60 MHz without compromising sensitivity. This combination of high sensitivity and wide bandwidth with no on-chip dissipation makes this device ideal for local sensing of spin dynamics, both classical and quantum.

Possible existence of field‐induced Josephson junctions

AbstractWe demonstrate the possible existence of a new class of superconducting Josephson junctions (JJs) named field‐induced Josephson junctions (FIJJs). One representative is a junction made by placing a ferromagnetic strip on the top of a superconducting strip, which we study in this work. We obtain a possible transition between one regime of an FIJJ, which is the quasi‐tunneling weak link Josephson junction (similar in certain aspects to an S–F–S Josephson junction, but with different boundary conditions), and the second regime of an FIJJ, which is the weak link constriction (two superconductors connected by a narrow superconducting link) as a function of the thickness of the superconducting strip, magnitude of magnetization, and temperature. We use the generalized Ginzburg–Landau (GL) equations derived from the extended Hubbard model in order to determine some properties of the new class of Josephson junction. In this paper, we perform the computation for a first type of superconductor, although both types of superconductor can be used to create an FIJJ. Further directions of studies of the indicated class of Josephson junction are also described.

Vertical SNS weak-link Josephson junction fabricated from only boron-doped diamond

A vertical superconductor/normal conductor/superconductor (SNS) weak-link Josephson junction has been successfully fabricated from only homoepitaxial diamond films. Superconducting diamond, normal-state diamond, and superconducting diamond are homoepitaxially grown in a sequence. The temperature dependence of the critical superconducting current was fitted using Likharev's theory of SNS weak-link junctions. When the normal-state-diamond thickness $L$ is much larger than the coherent length in the normal-state-diamond ${\ensuremath{\xi}}_{n}$, an exponential temperature dependence of normalized critical current was observed, indicating a proximity effect. Shapiro steps in the current-voltage characteristics under microwave irradiation were observed in the junction with $L\ensuremath{\gg}{\ensuremath{\xi}}_{n}$.

Fabrication of weak-link Nb-based nano-SQUIDs by FIB process

We develop a fabrication process of Nb-based nano-SQUIDs (superconducting quantum interference devices) containing two weak-link Josephson junctions patterned by a focused ion beam (FIB). Typical dimension of the SQUID diameter was 1μm, and the widths of the weak links were changed in the range of 60 and 500nm. In order to evaluate the degradation of Nb due to the FIB process, we employed bilayer films of Nb/Au and Nb/W in addition to single layer Nb films. The lateral degradation depths of 85nm for Nb and 27.5nm for Nb/Au and Nb/W indicate that the normal metals successfully work as the protection layer. The magnetic field dependence of the critical current showed the modulation ratio of about 10%.

Optimizing Anharmonicity in Nanoscale Weak Link Josephson Junction Oscillators

We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges with three dimensional banks have sufficient anharmonicity for realizing low noise amplifiers and quantum bits. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits with potentially higher quality factor than tunnel junction devices due to the absence of a lossy oxide layer.

On the Utilization of Magnetic Vector Potential for a Description of a Superconducting Transmission Line

We will present and examine an alternative approach to describe the behavior of superconducting transmission lines, and possibly weak link Josephson junction using the magnetic vector potential (A). While the utilization of magnetic vector potential is known in this field since the inception, a device level formulation based on A has not been fully investigated. We will show that for device level formulation, the magnetic vector potential is a mathematically simpler quantity to deal with than the combination of magnetic flux density (B) and electric field intensity (E) and still contains all the electromagnetic information of the junction under construction. In addition, other benefits of this formalism arise when dealing with Lagrangian and Hamiltonian mechanics. In this paper, we present a detailed description of how A can be determined for an infinite weak link Josephson junction with planar geometry. Utilizing the magnetic vector potential formulation, both electric and magnetic fields are calculated, and we show that we obtain the same dispersion relation as other approaches have previously demonstrated. We then discuss the advantages of this formalism. In addition, as an application of the present approach, we solve the Josephson junction's nonstationary equation numerically to get a realization of the actual coupling that occurs across the junction

Controlled-junction superconducting quantum interference device via phonon injection

The direct current superconducting quantum interference device (DC-SQUID), using controlled Josephson junction technology, provides a mechanism to modify the characteristics of the device post-fabrication. We report on the fabrication and measurement of a micron sized DC-SQUID using two Dayem bridge weak-link Josephson junctions with integrated “heaters.” The weak link critical current is controlled by hot phonons from the current biased titanium, normal metal heater. By using the heaters, control over the critical current oscillations of the SQUID was observed at 4.2K.

Hot phonon controlled-junction superconducting quantum interference device

The optimal design of a direct current superconducting quantum interference device (DC-SQUID) with high sensitivity requires two identical Josephson junctions, which is difficult to achieve. The design of a DC-SQUID using controlled Josephson junction technology provides a mechanism for modifying the characteristics of the device. Here we report on the nano-fabrication and measurement of a DC-SQUID utilizing two Dayem bridge weak-link Josephson junctions fabricated with a width ∼100 nm and a length of ∼200 nm. These junctions are controlled via the irradiation of hot phonons from nearby titanium/chromium normal metal constrictions which are current biased. The devices were measured at a temperature of 4.2 K and control over the critical current oscillations was observed.

Nonlinear microwave absorption in weak-link Josephson junctions.

A model, based on the resistively shunted junction theory, is developed and used to study microwave absorption in weak-link Josephson junctions in high-${T}_{c}$ superconductors. Both linear and nonlinear cases of microwave absorption in Josephson junctions are analyzed. A comparison of the model with microwave absorption loop theory is presented along with a general condition for the applicability of both models. The nonlinear case was solved numerically and the threshold points of sharp microwave absorption are presented. At these points, a $2\ensuremath{\pi}$ phase quantization takes place within each microwave cycle, leading to an onset of a sharp rise of absorption. Existence of the $2\ensuremath{\pi}$ dynamic quantization is the key to the interpretation of nonlinear microwave absorption data. The nonlinear microwave absorption model is extended to the study of nonuniformly coupled junctions, and a general statement for the applicability of such a model is presented.

A theoretically based critical-state model for granular high- Tc superconductors applied to YBCO

A critical-state model, based on a critical current density dependence on internal field J c ( H), which has been modeled for a random 3D network of weak-link Josephson junctions assumming spatial distribution of current in an individual grain- boundary junction (GBJ), is presented. The model is used in an analysis of isothermal magnetisation and pulse transport critical current measurements on sintered 123-YBCO superconducting material in the low-field “Josephson” regime. The analysis yields self-consistent agreement with experiment for both types of measurement. It also gives predictions for the superconducting parameters of the inter- and intra-granular material and yields some physical insights into the behaviour of the junctions. In particular, there exists a field-independent component of the inter-granular critical current which depends on the GBJ microstructure. In the present specimen material it generally increases with decreasing temperature but shows a marked increase at about 60 K corresponding to the onset of superconductivity in the 60 K oxygen-deficient phase in the GBJ.

Effect of grain boundaries on magnetic field penetration in polycrystalline superconductors.

The magnetic-field penetration at grain boundaries in superconductors is calculated using a model in which the grains and the grain boundaries are treated on an equal basis. The grains are modeled using the London theory, and the grain boundaries as weak-link Josephson junctions in the linear regime. An exact solution is found. Calculations of the overall effective penetration depth are presented for regular laminar arrays of grain boundaries for arbitrary grain size, diagonal grain anisotropy, and grain boundary coupling. Analytical formulas are obtained in several limiting cases, and simple empirically fit formulas are presented that are applicable in most intermediate regimes of grain size and grain coupling. The relevance of the results to the high-temperature oxide superconductors is discussed.

Oscillation modes in the tunnel type and the weak-link type Josephson junctions

The present paper discusses in detail the oscillation modes and these dependency on system parameters in the tunnel type and weak-link type Josephson junctions driven by dc and rf current sources.

Dc SQUID Microwave-Induced Characteristics and Magnetic Field Response, Derived Using the Stewart-McCumber Model

This paper describes the I-V characteristics (as a function of applied magnetic field) and magnetic field response of a dc SQUID which incorporates two weak-link Josephson junctions in a superconducting ring. These characteristics are derived by digital computer simulation, using the Stewart-McCumber model. The effects of asymmetry (dissimilarity between the junctions) on SQUID critical current Ic, normal resistance R and capacitance C are also simulated. With microwave excitation applied, the Josephson oscillations of the dc SQUID are found to be “frequency-locked” to the applied microwave signal even when critical currents Ic of the two junctions differed, Subharmonic voltage steps are obtained for a symmetric dc SQUID in a magnetic field even when the current-phase relationship is purely sinusoidal.

Fabrication of the Weak-Link Josephson Junction on a Microstep

Fabrication of the Weak-Link Josephson Junction on a Microstep

Voltage steps in the current-induced resistive state of thin-film type-I superconductors

We report the observation of voltage steps in the current-induced resistive state in superconducting strips of lead and indium. The strips were 1.7-6 mm long, 0.1-8.0 \ensuremath{\mu}m thick, and 100-300 \ensuremath{\mu}m wide. The voltage steps are attributed to the nucleation of trains of flux tubes moving rapidly from the edge to the center of the strip. In the center, opposite tubes arriving from opposite edges annihilate each other. The moving flux-tube trains are, obviously, the outgrowth to the case of a three-dimensional type-I superconductor of the dynamic behavior of the weak-link Josephson junction, and, in particular, of the Anderson-Dayem bridge. From a simple eddy-current-damping model we have estimated the number of flux tubes existing simultaneously in a single flux-tube train.