Josephson Network Research Articles

Multiterminal Inverse AC Josephson Effect.

When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect─the phase of the junction locks to the drive frequency. As a result, the I-V curves of the junction acquire "Shapiro steps" of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multiterminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest that multiterminal Josephson junctions are a playground to study highly connected nonlinear networks with novel topologies.

Order Parameter in Electron System: Its Fluctuations and Oscillations

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.

Quantum phase slips and number-phase duality in disordered TiN nanostrips

We have measured the electric transport properties of TiN nanostrips with different widths. At zero magnetic field the temperature dependent resistance R(T) saturates at a finite resistance towards low temperatures, which results from quantum phase slips in the narrower strips. We find that the current-voltage (I-V) characteristics of the narrowest strips are equivalent to those of small Josephson junctions. Applying a transverse magnetic field drives the devices into a reentrant insulating phase, with I-V-characteristics dual to those in the superconducting regime. The results evidence that our critically disordered superconducting nanostrips behave like small self-organized random Josephson networks.

ORDER PARAMETER IN ELECTRON SYSTEMS: ITS FLUCTUATIONS AND OSCILLATIONS

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.

Networks of Josephson junctions and their synchronization

One can demonstrate that a 1-D Josephson network containing junctions with different resistances can be synchronized at frequencies, which are multiples of 2eV, where V is the total d.c. voltage applied across the network. The appearance of such synchronization follows from the law of charge conservation and takes place if charge transfer is dominated by the Josephson channel. One can observe also a sub-harmonic structure. The result holds for cluster-based arrays as well as for general case of a tunneling network.

Multiple order parameter configurations in superconductor/ferromagnet multilayers

The coupling of two superconductors (S) through a ferromagnet (F) can lead to either a zero- or a $\ensuremath{\pi}$-phase difference between the superconducting banks. Most research in this area is performed on trilayer S/F/S film structures, in which two-order parameter configurations are possible. Increasing the number of layers and junctions leads to a larger number of possible configurations with, in principle, different properties such as the superconducting transition temperature ${T}_{c}$. Here we study the behavior of a series of multilayers made of superconducting Nb and ferromagnetic Pd${}_{81}$Ni${}_{19}$. We find that for the individual layer thicknesses used, the transition width $\ensuremath{\Delta}{T}_{c}$ increases with increasing number of bilayers in the multilayer, in a well-defined manner. That the broadening is not simply due to increased disorder in the larger stacks, it is shown from x-ray diffraction, which finds very sharp interfaces for all samples; and from the effect of the magnetic field on the transition, which shows a considerable sharpening. We can make a connection with the various order parameter configurations using a matrix formulation of quasiclassical theory based on the Usadel equations and show that these different configurations take part in the Josephson networks, which are building up in the transition to the superconducting state.

Unusually strong coherent response from grain-boundary Josephson network in polycrystalline Pr x Y1 − x Ba2Cu3O7 − δ

By applying a highly sensitive homemade AC susceptibility technique to Pr_{x}Y_{1-x}Ba_2Cu_3O_7 polycrystals (with x=0.0, 0.1 and 0.3), we observed very sharp Fraunhofer type low-field periodic oscillations of the real part of the AC susceptibility which were attributed to Josephson vortices penetrating intergranular regions of grain-boundary Josephson network in our samples. Assuming the Lorentz type distribution of single-junction contact areas, we were able to successfully fit the experimental data.

Spatial Development of Superconductivity in the Sr2RuO4–Ru Eutectic System

We have clarified how the enhanced superconductivity, often referred to as the 3-K phase superconductivity, develops in the Sr2RuO4-Ru eutectic system. From the detailed ac and dc susceptibility measurements on well-characterized crystals, we revealed strongly anisotropic shielding, governed by the direction of the screening current dominated within the RuO2 plane rather than by the orientation of the Ru lamellae. The onset temperature of the 3-K phase superconductivity probed by diamagnetic screening is as high as 3.5 K. The temperature dependence of the diamagnetic shielding above around 2 K is well ascribed by the interfacial screening around each Ru lamella. Below around 2 K, the rapid development of the shielding fraction as well as its peculiar esponse to ac and dc magnetic fields are explained by the formation of the Josephson network consisting of inter-lamellar supercurrents.

Frustration of decoherence in Y-shaped superconducting Josephson networks

We examine the possibility that pertinent impurities in a condensed matter system may help in designing quantum devices with enhanced coherent behaviors. For this purpose, we analyze a field theory model describing Y-shaped superconducting Josephson networks. We show that a new finite coupling stable infrared fixed point emerges in its phase diagram; we then explicitly show that, when engineered to operate near this new fixed point, Y-shaped networks support two-level quantum systems, for which the entanglement with the environment is frustrated. We briefly address the potential relevance of this result for engineering finite-size superconducting devices with enhanced quantum coherence. Our approach uses boundary conformal field theory since it naturally allows for a field-theoretical treatment of the phase slips (instantons), describing the quantum tunneling between degenerate levels.

Concentric circular arrays of Josephson junctions as dressed models of granular superconductors

An extended dressed Josephson network model is adopted to study the quantitative magnetic behaviour of three-dimensional granular systems. The model consists of a stack of collections of N concentric circular arrays of small identical Josephson junctions, each two adjacent elements of the stack being superconductively coupled by additional Josephson junctions. The low-field magnetic response of granular superconductors is simulated by means of the proposed model.

Topology-induced critical current enhancement in Josephson networks

Abstract We investigate the properties of Josephson junction networks with inhomogeneous architecture. The networks are shaped as “square comb” planar lattices on which Josephson junctions link superconducting islands arranged in the plane to generate the pertinent topology. Compared to the behavior of reference linear arrays, the temperature dependencies of the Josephson currents of the branches of the network exhibit relevant differences. The observed phenomena evidence new and surprising behavior of superconducting Josephson arrays.

Nonlinear microwave properties of YBa2Cu3O7−x block epitaxial films near the superconducting transition temperature

The structure and local properties of a nonlinear microwave response of YBa{sub 2}Cu{sub 3}O{sub 7-x} block films, as well as microbridges of these films, are studied using low-temperature scanning microscopy. Correlation between the halfwidth of the temperature dependence of the third harmonic power W{sub TH} and the curve of the electron-beam induced voltage W{sub EBIV} is observed for the medium size of the block. A theoretical model is proposed, which demonstrates that the nonlinear microwave response for large blocks is determined by intrablock pinning of Abrikosov vortices; for blocks of smaller size, the response acquires an additional contribution associated with pinning of hypervortices on the Josephson network of the boundaries between the blocks.

Josephson Network as a Model for Inhomogeneous Superconductor: a Microwave Power Absorption

We discuss the applied magnetic field dependence of the microwave absorption by a three-dimensional array of up to 30 × 30 × 30 Josephson junctions with random parameters including the resistivity, capacity, and inductance of each junction. The numerical simulation results for the networks show characteristic microwave absorption anomalies observed in the ceramic samples of high temperature superconductor YBa2Cu3O7−x. We also provide a discussion of the absorption in simple analytical terms of the Josephson loop instabilities.

Rocking Ratchets in Two-Dimensional Josephson Networks: Collective Effects and Current Reversal

A detailed numerical study on the directed motion of ac-driven vortices and antivortices in 2D Josephson junction arrays with an asymmetric periodic pinning potential is reported. dc-voltage rectification shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with ac amplitude for a wide range of vortex density around f = 1/2 (f = Ha(2)/Phi(0)), in good agreement with recent experiments by Shalóm and Pastoriza [Phys. Rev. Lett. 94, 177001 (2005)10.1103/PhysRevLett.94.177001]. The study of vortex structures, spatial and temporal correlations, and vortex-antivortex pairs formation gives insight into a purely collective mechanism behind the current reversal effect.

Effect of the microstructure of epitaxial YBa2Cu3O7 − x films on their electrophysical and nonlinear microwave properties

The local nonlinear microwave response of YBa2Cu3O7 − x films was measured by near-zone field microscopy with a spatial resolution of 50 μm, and YBa2Cu3O7 − x film microbridges were locally studied by low-temperature scanning microscopy with a spatial resolution of 4 μm. The microstructure of epitaxial YBa2Cu3O7 − x films was examined using x-ray diffraction and electron microscopy. A correlation is detected between the average crystallite size and the half-widths of the temperature dependences of the third-harmonic power (W TH) and the electron-beam-induced voltage (W EBIV). The experimental results are described in terms of a model of a two-phase medium taking into account the nonlinear I-V characteristic of the superconductor. For large crystallites, the nonlinear microwave response is shown to be caused by intracrystallite vortex pinning. As the average crystallite size decreases, an additional contribution to the nonlinear response appears due to the pinning of a magnetic flux by the Josephson network of crystallite boundaries. Calculations show that a three-fold increase in the crystallite size decreases the nonlinearity coefficient of YBa2Cu3O7 − x films by two orders of magnitude.

Anomalous Josephson network in theRu‐Sr2RuO4eutectic system

We measured the $c$-axis current-voltage $(I\text{\penalty1000-\hskip0pt}V)$ characteristics of ${\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ and Ru-enriched ${\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ eutectic systems. Our results revealed that the 3-K phase in the $\mathrm{Ru}\text{\penalty1000-\hskip0pt}{\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ eutectic system forms a complex Josephson network, which dominates the critical current of the system even at temperatures below bulk ${T}_{c}$. We also found that this Josephson network exhibits anomalous asymmetric features in $I\text{\penalty1000-\hskip0pt}V$ characteristics, such that the critical current density at positive current ${J}_{c}^{\phantom{\rule{0.2em}{0ex}}+}$ differs from that at negative current ${J}_{c}^{\phantom{\rule{0.2em}{0ex}}\ensuremath{-}}$ by 5% at 0.3 K. This unusual behavior diminishes with increasing temperature or magnetic field. It disappears at temperatures above 2.3 K at zero field, or above 0.2 T at 0.3 K. We discuss these unusual behaviors in terms of a recent theory that argues a time reversal symmetry breaking transition in the 3-K phase.

TOPOLOGY INDUCED MACROSCOPIC QUANTUM COHERENCE IN JOSEPHSON JUNCTION NETWORKS

We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamical properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose–Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose–Einstein condensation for Josephson networks built on comb graphs.

Proximity effect in the superconducting magnetization of a Pb/Cu bilayer film with an antidot lattice

AC magnetization measurements are reported for a superconducting Pb (500 Å)/Cu (100 Å) film bilayer with a triangular lattice of antidots of diameter D=0.35 μm and spacing d=1.0 μm. Sharply peaked magnetization anomalies occur at applied DC magnetic fields H n = nH 1, where 1⩽ n⩽3, and H 1=24 Oe is the first “matching field” at which every antidot traps exactly one fundamental flux quantum Φ 0. The peaked nature of the matching anomalies is similar to the behavior of Josephson networks (having d/ D≈1), but differs from more step-like structures observed in the magnetization of other patterned films with d/ D≫1. The n=3, 4 matching anomalies successively disappear when the applied field is tilted away from the bilayer normal by 70–84°. The peaked magnetization, low transition temperature of 6.70 K, reduced angular stability of the flux lattice, and the absence of clear matching anomalies with n>4, indicate that these properties are novel probes of a proximity effect between normal (Cu) and superconducting (Pb) film layers.

Percolating granular superconductors.

We investigate diamagnetic fluctuations in percolating granular superconductors. Granular superconductors are known to have a rich phase diagram including normal, superconducting, and spin-glass phases. Focusing on the normal-superconducting and the normal-spin-glass transition at low temperatures, we study the diamagnetic susceptibility chi((1)) and the mean square fluctuations of the total magnetic moment chi((2)) of large clusters. Our work is based on a random Josephson network model that we analyze with the powerful methods of renormalized field theory. We investigate the structural properties of the Feynman diagrams contributing to the renormalization of chi((1)) and chi((2)). This allows us to determine the critical behavior of chi((1)) and chi((2)) to arbitrary order in perturbation theory.

Pressure dependence of chiral-glass transition in Y–Ba–Cu–O ceramics

Ceramic high-TC superconductors may be viewed as a weakly coupled random Josephson network containing the so-called π-junctions, and a chiral-glass transition is predicted to be occurred in such d-wave ceramics. In the present work, pressure dependence of the chiral-glass transition have been investigated on YBa2Cu3O7−y and YBa2Cu4O8 ceramics. With decreasing temperature, a superconducting order occurs at first inside each grain at TC1 and furthermore among the grains at TC2 (<TC1). The TC2 increases with increase of pressure, while the sharpness of the transition at TC2 does not change. In spite of differences in not only TC2’s but also TC1’s, the increasing rates of TC2 by pressure are nearly the same.