The shape of a moving fluxon in stacked Josephson junctions

We study numerically and analytically the shape of a single fluxon moving in a double stacked Josephson junctions (SJJ's) for various junction parameters. We show that the fluxon in a double SJJ's consists of two components, which are characterized by different Swihart velocities and Josephson penetration depths. The weight coefficients of the two components depend on the parameters of the junctions and the velocity of the fluxon. It is shown that the fluxon in SJJ's may have an unusual shape with an inverted magnetic field in the second junction when the velocity of the fluxon is approaching the lower Swihart velocity. Finally, we study the influence of fluxon shape on flux-flow current-voltage characteristics and analyze the spectrum of Cherenkov radiation for fluxon velocity above the lower Swihart velocity. Analytic expression for the wavelength of Cherenkov radiation is derived.Comment: 12 pages, 12 figure

Influence of the passive region on Zero Field Steps for window Josephson junctions

We present a numerical and analytic study of the influence of the passive region on fluxon dynamics in a window junction. We examine the effect of the extension of the passive region and its electromagnetic characteristics, its surface inductance and capacitance. When the velocity in the passive region $v_{I}$ is equal to the Swihart velocity (1) a one dimensional model describes well the operation of the device. When $v_{I}$ is different from 1, the fluxon adapts its velocity to $v_{I}$. In both cases we give simple formulas for the position of the limiting voltage of the zero field steps. Large values of inductance and capacitance lead to different types of solutions which are analyzed.Comment: 12 pages, 13 figure

Influence of Josephson current second harmonic on stability of magnetic flux in long junctions

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The dependence of the static magnetic flux distributions on parameters of the model are investigated numerically. Stability of the static solutions is checked by the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New solutions which do not exist in the traditional model, have been found. Investigation of the influence of second harmonic on the stability of magnetic flux distributions for main solutions is performed.Comment: 4 pages, 6 figures, to be published in Proc. of Dubna-Nano2010, July 5-10, 2010, Russi

Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results, in terms of elliptic functions in the case of inline geometry, are in agreement with the numerical calculations and explain the strong hysteretic phenomena typically seen in the calculation of the maximum tunneling current. This suggests a different experimental approach based on the use, instead of the external magnetic field the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behavior and unfold the overlapping $I_{max}(H)$ curves.Comment: 36 pages with 17 figure

Flux Flow Effects in Annular Josephson Tunnel Junctions

We investigate Josephson flux-flow in annular Josephson tunnel junctions (AJTJs) under the application of magnetic fields generating finite-voltage steps in their current-voltage characteristics. Experimental data are presented for confocal AJTJs which are the natural generalization of the well studied circular AJTJs for which flux flow effects have never been reported. Displaced linear slopes, Fiske step staircases and Eck steps were sequentially recorded at $4.2\,K$ with high-quality Nb/Al-AlOx/Nb confocal AJTJs when increasing the strength of a uniform magnetic field applied in the plane of the junction. Their amplitude was found to strongly depend not only on the strength, but also on the orientation, of the external field. Extensive numerical simulations based on a phenomenological sine-Gordon model developed for confocal AJTJs were carried out to disclose the basic flux-flow mechanism responsible for the appearance of magnetically induced steps and to elucidate the role of several critical parameters, namely, the field orientation, the system loss and the annulus eccentricity. It was found that in a topologically closed system, such as the AJTJ, where the number of trapped fluxons is conserved and new fluxons can be created only in the form of fluxon-antifluxon pairs, the existence of a steady viscous flow of Josephson vortices only relies on the capability of the fluxons and antifluxons to be generated and to annihilate each other inside the junction. This also implies that flux-flow effects are not observable in circular AJTJs.Comment: 26 pages, 8 figure

Sine-Gordon breathers generation in driven long Josephson junctions

We consider a long Josephson junction excited by a suitable external ac-signal, in order to generate control and detect breathers. Studying the nonlinear supratransmission phenomenon in a nonlinear sine-Gordon chain sinusoidally driven, Geniet and Leon explored the bifurcation of the energy transmitted into the chain and calculated a threshold $A (\omega)$ for the external driving signal amplitude, at which the energy flows into the system by breathers modes. I numerically study the continuous sine-Gordon model, describing the dynamics of the phase difference in a long Josephson junction, in order to deeply investigate the "continuous limit" modifications to this threshold. Wherever the energy flows into the system due to the nonlinear supratransmission, a peculiar breather localization areas appear in a $(A, \omega)$ parameters space. The emergence of these areas depends on the damping parameter value, the bias current, and the waveform of driving external signal. The robustness of generated breathers is checked by introducing into the model a thermal noise source to mimic the environmental fluctuations. Presented results allows one to consider a cryogenic experiment for creation and detection of Josephson breathers.Comment: 8 pages, 3 figure

Critical currents in Josephson junctions with macroscopic defects

The critical currents in Josephson junctions of conventional superconductors with macroscopic defects are calculated for different defect critical current densities as a function of the magnetic field. We also study the evolution of the different modes with the defect position, at zero external field. We study the stability of the solutions and derive simple arguments, that could help the defect characterization. In most cases a reentrant behavior is seen, where both a maximum and a minimum current exist.Comment: 17 pages with 16 figures, submitted to Supercond. Sci. Techno