Fluxon Motion Research Articles

Fluxons in thin-film superconductor-insulator superlattices

In a system of thin alternating layers of superconductors and insulators the equations describing static and dynamic fluxon solutions are derived. The approach, represented by a useful compact matrix form, is intended to describe systems fabricated for example of niobium or niobium-nitride thin films; in the limit of ultrathin superconductor films it may give a model for describing fluxon motion in layered high-Tc superconductors. Numerical examples of current versus voltage curves to be expected in such an experiment are presented.

Detection of mm and submm wave radiation from soliton and flux-flow modes in a long Josephson junction

The authors report on the coupling of millimeter and submillimeter waves from a long (3- mu m*350- mu m) Josephson junction to a small (2- mu m*2- mu m) superconductor-insulator-superconductor (SIS) junction by using a center-fed interdigital capacitor. Coupled power at around 100 GHz and 261 GHz was observed. Experiments confirm that the critical current density j/sub c/ of a long junction determines the fluxon motion. Coupled irradiation (>3nW) at around 100 GHz, which corresponds to resonant soliton oscillations in low j/sub c/ samples (250 A/cm/sup 2/ to 1000 A/cm/sup 2/), is detected by the SIS junction. The incident power to the SIS detector junction could be tuned with only little frequency pulling by adjusting the current bias of the oscillator. For j/sub c/>1000 A/cm/sup 2/, coupled radiation at around 100 GHz (about 3 nW) and 261 GHz (4.6 nW), from flux-flow oscillations, is also clearly seen. Flux-flow radiation at 350 GHz is also observed. It is concluded that a large j/sub c/ value is preferable for high-frequency flux-flow oscillators.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamics of rotationally symmetric solitons in the near-SG field model with application to fluxon motion in a large area Josephson junction: a collective-coordinate description

The dynamics of the ( n+1)-dimensional rotationally symmetric sine-Gordon solitons of large radius under potential perturbations and dissipative pertubations as well, is considered by means of a perturbation treatment based on a collective-coordinate description of the solution and the Lagrangian variational method. The particle-like character of a soliton is emphasized. The equation of soliton motion and, in particular, the generalized momentum of the soliton are obtained in a canonical manner. All kinds of dynamical regimes in the phase space that correspond to various initial conditions are explored. In the presence of dissipation, the corrected equation of soliton motion is obtained from the generalized variation method. Finally the application of the theoretical treatment is considered for the solitons (or fluxons) in a circularly symmetric Josephson junction, and the analytical results are examined by direct numerical simulations with fairly good agreement.

Shapiro steps in the fluxon motion in superconductors.

A method for studying the fluxon motion in superconductors is suggested based on so-called Shapiro steps in the current-voltage characteristics. These are similar to ones that appear in Josephson junctions. A knowledge of the properties of Shapiro steps would provide important information on the properties of fluxons. An exact, nonperturbative calculation of the sizes of Shapiro steps is given for a periodic field having the form of a symmetric pulse.

Dynamics of sine-Gordon solitons in the annular Josephson junction.

The annular Josephson junction allows for the study of undisturbed soliton (fluxon) motion in the absence of collisions. With new experimental methods and design we have realized for the first time a fully controllable way of introducing individual fluxons or antifluxons into such a system. This has allowed us to study multisoliton behavior and to make a comparison with existing soliton-chain perturbation theory. An unforeseen crossover in the dynamical behavior at high velocities is tentatively interpreted in terms of soliton bunching.

Phase-locking of soliton motion in uniformly driven sine-Gordon systems

Phase-locking of fluxon motion in a long, but finite, Josephson junction is studied analytically in the case where the external forces are uniformly distributed in space. The range of phase-locking in bias current is found and it is demonstrated that the mechanism of locking can be described as a boundary effect. We find very good agreement between the analytical results and results of direct numerical simulations of the problem.

Effect of thermal noise on the phase locking of a Josephson fluxon oscillator.

The influence of thermal noise on fluxon motion in a long Josephson junction is investigated when the motion is phase locked to an external microwave signal. It is demonstrated that the thermal noise can be treated theoretically within the context of a two-dimensional map that models the dynamics of a single fluxon.

Flux-creep dissipation in Y-Ba-Cu-O superconductors at microwave frequencies.

Microwave measurements of the absorbed power in granular Y-Ba-Cu-O samples for temperatures in the range 1--50 K are reported. The hysteretic behaviors observed are attributed to the fluxon motion in the flux-creep regime. A calculation of the surface resistance, based on the hypothesis of validity of the Bean model and which qualitatively explains the experimental results, is given. The potential of the surface-resistance measurement technique at microwave frequencies to detect various types of losses (flux creep, flux flow, and Josephson-junction dephasing) is discussed.

Fluxons and superfluxons in Josephson junctions with periodical structure of the magnetic inclusions

The motion of fluxons in Josephson junctions with periodical systems of structure defects with a magnetic moment is investigated. A new type of fluxon pinning, namely the pinning outside the defects, is predicted. The dependence of the critical current on the external magnetic field and distance between defects has been obtained. It is shown that in the case of a fast fluxon its interaction with the magnetic defect is only magnetic. The existence of supersolitons in the fluxon chains is predicted. The results of the theory is used to explain the dependence of critical current on the magnetic field in high temperature superconductors.

Anisotropic viscous flux motion in high-T c superconducting films

We have studied the microwave transmission through thin Y-Ba-Cu-O films in the presence of magnetic field and for different field orientation with respect to the crystallographic c - axis. We demonstrate that such measurements yield the anisotropy of the viscosity coefficient for fluxon motion, η. We found experimentally that the ratio η a ( c) /η c ( a) is temperature independent and equals to ≈4–6 for T c > T> 0.8T c (here η j ( i) represents motion along the j- axis of a fluxon oriented along the i -axis). This allows an estimate of the effective mass ratio γ = (m c m a) 1 2 ≈ 5–8 , using recent theories.

Microwave transmission and harmonic generation in granular high-Tc superconducting films: Evidence for viscous flux motion and weak links.

We have studied the microwave transmission \ensuremath{\tau} through thin superconducting films of Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O in the presence of a dc magnetic field ${\mathrm{H}}_{0}$ and an alternating magnetic field, ${\mathrm{H}}_{1}$cos2\ensuremath{\pi}${\mathrm{f}}_{0}$t. The alternating field generates many harmonics due to the nonlinear response of the complex resistivity. The microwave transmission with ${\mathbf{H}}_{0}$ in the plane of the film depends on the orientation \ensuremath{\Phi} of ${\mathbf{H}}_{0}$ with respect to the microwave electric field. We found experimentally that the field-dependent part of the transmission behaves like \ensuremath{\delta}${\mathrm{\ensuremath{\tau}}}_{\mathrm{f}}$\ensuremath{\propto}|${\mathrm{H}}_{0}$sin\ensuremath{\Phi}|. This indicates a macroscopic Lorentz force and strongly suggests that the complex resistivity in the magnetic field is dominated by a viscous-flux-motion dissipation mechanism. We demonstrate a simple model for the harmonic generation based on viscous fluxon motion. A comparison of the experiment with the model allows an estimate of the viscosity coefficient \ensuremath{\eta} for the fluxons in the direction of the c axis to be \ensuremath{\eta}=( 2--4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ cgs units for Y-Ba-Cu-O film at T=70 K. Theoretical models suggest that the magnitude of \ensuremath{\eta} is appropriate to weakly pinned Abrikosov fluxons. The dc transport properties of superconducting films containing internal Josephson junctions are strongly affected by microwave irradiation and serve, therefore, as a diagnostic tool to detect the presence of ``weak links.'' Higher-order harmonics can be generated in all types of studied films independent of the presence or absence of weak links. However, in the presence of weak links, the onset temperature for the harmonic generation ${\mathrm{T}}_{\mathrm{c}}^{\ensuremath{'}}$ is lower than the onset temperature for the change in the microwave transmission, ${\mathrm{T}}_{\mathrm{c}}$. A simple model based on the granularity of the film can explain these observations.

Multi-fluxon steps in long Josephson junctions and their application to oscillators

Studies of long NbN Josephson junctions of the overlap type in the presence of an external magnetic field show constant voltage steps of the Fiske type, and large voltage steps. The latter are attributed to multifluxon resonances within the cavity of the junction. The multifluxon steps correspond to bunches of fluxons introduced in the junction because the junction electrode thicknesses are comparable to the penetration depth. These steps are very sharp, and they have large current amplitudes. When biased at such constant voltage steps, the device can be a resonant mode oscillator. The power and frequency are determined by the mode of fluxon motion inside the junction.

Phase-locking of long annular Josephson junctions coupled to an external rf magnetic field

Phase-locking of fluxon motion in a long annular Josephson junction coupled to an external magnetic field is demonstrated. applying a simple perturbation method to the perturbedj sine-Gordon system, which models the long Josephson junction. The perturbation result is compared to results of numerical solution of the perturbed sine-Gordon system and good agreement is found.

Flux creep in Josephson junction arrays

In order to analyze the diamagnetic properties of weakly coupled structures in high-T/sub c/ ceramic superconductors , the Josephson junction array model is used. It is suggested that the coupling is strong enough to allow magnetic flux trapping inside nonsuperconducting regions surrounded by superconducting loops closed by Josephson junctions. It is noted that the presence of currents flowing through the junctions has to be taken explicitly into account in the Hamiltonian. This description leads to a creep model of the Josephson junctions array. As a result, one observes the following: (1) pinning centers generated by nonsuperconducting regions into the loops, (2) pinning potentials determined by fluxon motion barriers due to the Josephson junctions, (3) absence of degeneracy of the states corresponding to a different number of fluxons in the loops, and (4) a reduction of the barrier height due to measuring currents or to diamagnetic shielding currents. The last effect is equivalent to the Lorentz force effect in type-II semiconductors. Thus, it is believed that this picture greatly modifies the usual superconducting glass model.

Numerical study of long Josephson junctions coupled to a high-Q cavity.

Long Josephson junctions coupled to a high-Q resonator are studied numerically and compared with recently published approximative results, obtained by using a perturbative approach to the fluxon motion in the junction. The similarities and differences in the two approaches are discussed.

Microwave loss and oxygen annealing in YBa2Cu3Ox single crystals.

Reversible thermal annealing of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{x}}$ single crystals in air has been studied by microwave loss measurements. Among the advantages of this contactless technique are the following: Crystals are kept in sealed capillaries throughout cycles of annealing and low-temperature measurement; features are resolved in loss versus temperature measurements that are not revealed by other techniques. Microwave loss is interpreted in terms of the Gittleman-Rosenblum model of fluxon motion in a viscous medium. Narrow temperature ranges are found for the formation of the 60- and 90-K phases. Optimal microwave response is obtained after but a few hours of annealing, indicating the importance of c-axis diffusion.

Josephson junction dynamics in the presence of inhomogeneities

We study the motion of fluxons in a long Josephson junction with two pointlike inhomogeneities (or impurities). Using the collective variable approach, we reduce the problem to two nonlinear o.d.e.'s and find that the behavior of the fluxons depends on the location of the invariant manifolds of two unstable fix points near the two inhomogeneities. Thus varying the “strength” parameters of the inhomogeneities μ 1 and μ 2 we can make these invariant manifolds “pass through” each other and allow fluxon trapping or escape by the impurities accordingly. Our results can be easily extended to the case of N inhomogeneities and have been found to agree very well with the numerical solution of the original p.d.e. of the problem.

Flux pinning and scaling laws for superconducting V3Ga

The electric field versus current density (E-J) characteristics of a multifilamentary V3Ga wire are presented for temperatures in the range 2.5 K≤T≤Tc in magnetic fields up to 15 T. The critical current density (Jc) is determined throughout the superconducting phase for this composite. The volume pinning force (Fp=Jc×B) obeys the Fietz–Webb scaling law which is of the separable form Fp=αBnc2(T)f(b), where Bnc2(T) is a function only of temperature and f(b) is a function only of reduced field b [b=B/Bc2(T)]. In addition, two other scaling laws of this separable variable form which characterize the variation of critical current densities throughout the sample and the flux flow state are explicitly determined. It is demonstrated that similarly to NbTi and Nb3Sn, the mechanism describing dissipation above Jc must incorporate the intermittent motion of fluxons or flux bundles across the superconductor such that only a fraction (∼10−5) of the flux-line lattice is in motion.

Magnetic field modulation dependence of zero field microwave response in the high-T c superconductor YBa 2Cu 3O 6.93

Microwave absorption in the vicinity' of zero magnetic field (zero field peak) has been measured for high-T c superconductor, YBa 2Cu 3O 6.93 at the first and second harmonic of modulation field. The effects observed for small amplitudes of modulation (H m) have been discussed and related to the model of damped motion of free fluxons. The real component of a complex surface impedence for small H m has been estimated and correlated with the lineshape of the zero field peak detected at the first harmonic. An anomalous behaviour of the lineshape detected at this harmonic is found to have a source in the dispersion contribution and in the magnetic structure of this material.

Flux creep and critcal-current anisotropy in Bi2Sr2CaCu2O8+ delta.

We have studied magnetic relaxation, temperature dependence of the critical currents, magnetic irreversibility, and lower critical fields in single crystals of the high-${T}_{c}$ superconductor ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ (idealized composition) through magnetization measurements. The results are analyzed within the framework of the critical state and a thermally activated flux-creep model. The results indicate three different critical curents and flux-creep rates depending on the relative orientation of the current, the field, and the Cu-O planes. The flux-creep rate for flux lines moving perpendicular to the planes, was found to be unobservably low. Similarly, the critical current density perpendicular to the planes was very low. However the critical current density in the plane and the flux-pinning well depth ${U}_{0}$, for fluxon motion parallel to the planes, are similar to the values found in Y-Ba-Cu-O. Implications of insulating layers between the Cu-O planes are discussed.