Yu. M. Shukrinov

Investigation of the breakpoint region in stacks with a finite number of intrinsic Josephson junctions

We study the breakpoint region on the outermost branch of current-voltage characteristics of the stacks with different number of intrinsic Josephson junctions. We show that at periodic boundary conditions the breakpoint region is absent for stacks with even number of junctions. For stacks with odd number of junctions and for stacks with nonperiodic boundary conditions the breakpoint current is increased with number of junctions and saturated at the value corresponding to the periodic boundary conditions. The region of saturation and the saturated value depend on the coupling between junctions. We explain the results by the parametric resonance at the breakpoint and excitation of the longitudinal plasma wave by the Josephson oscillations. A way for the diagnostics of the junctions in the stack is proposed.

Diffusion current in a system of coupled Josephson junctions

The role of a diffusion current in the phase dynamics of a system of coupled Josephson junctions (JJs) has been analyzed. It is shown that, by studying the temporal dependences of the superconducting, quasi-particle, diffusion, and displacement currents and the dependences of average values of these currents on the total current, it is possible to explain the main features of the current-voltage characteristic (CVC) of the system. The effect of a diffusion current on the character of CVC branching in the vicinity of a critical current and in the region of hysteresis, as well as on the part of CVC branch corresponding to a parametric resonance in the system is demonstrated. A clear interpretation of the differences in the character of CVC branching in a model of capacitively coupled JJs (CCJJ model) and a model of capacitive coupling with diffusion current (CCJJ+DC model) is proposed. It is shown that a decrease in the diffusion current in a JJ leads to the switching of this junction to an oscillating state. The results of model calculations are qualitatively consistent with the experimental data.

Devil's staircases and continued fractions in Josephson junctions

The detailed numerical simulations of the IV-characteristics of Josephson junction under external electromagnetic radiation show devils staircases within different bias current intervals. We have found that the observed steps form very precisely continued fractions. Increasing of the amplitude of radiation shifts the devils staircases to higher Shapiro steps. The algorithm of appearing and detection of the subharmonics with increasing radiation amplitude is proposed. We demonstrate that subharmonic steps registered in the famous experiments by A. H. Dayem and J. J. Wiegand [Phys. Rev 155, 419 (1967)] and J. Clarke [Phys. Rev. B 4, 2963 (1971)] also form continued fractions.

Structured chaos in a devil's staircase of the Josephson junction

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devils staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devils staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Modeling of tunneling spectroscopy in high-TC superconductors

The tunneling density of states of high-Tc superconductors is calculated taking into account the tight-binding band structure, group velocity, and tunneling directionality for s-wave and d-wave gap symmetry. The characteristic density of states has asymmetry of the quasiparticle peaks, flat s-wave and cusplike d-wave subgap behavior, and an asymmetric background. It is assumed that the underlying asymmetry of the conductance peaks is primarily due to the features of the quasiparticle energy spectrum and that the d-wave symmetry enhances the degree of asymmetry of the peaks. Increasing the lifetime broadening factor changes the degree of asymmetry of the tunneling conductance peaks and leads to confluence of the quasiparticle and van Hove singularity peaks.

Phase dynamics of two parallel stacks of coupled Josephson junctions

Two parallel stacks of coupled Josephson junctions (JJs) are investigated to clarify the physics of transitions between the rotating and oscillating states and their effect on the IV-characteristics of the system. The detailed study of phase dynamics and bias dependence of the superconducting and diffusion currents allows one to explain all features of simulated IV-characteristics and demonstrate the correspondence in their behavior. The coupling between JJ in the stacks leads to the branching of IV-characteristics and a decrease in the hysteretic region. The crucial role of the diffusion current in the formation of the IV-characteristic of the parallel stacks of coupled JJs is demonstrated. We discuss the effect of symmetry in a number of junctions in the stacks and show a decrease of the branching in the symmetrical stacks. The observed effects might be useful for development of superconducting electronic devices based on intrinsic JJs.

Parametric resonance in the system of long Josephson junctions

The phase dynamics of the system of long Josephson junctions whose length exceeds the Josephson penetration depth has been studied. The possibility of the appearance of a longitudinal plasma wave and parametric resonance has been demonstrated. Both inductive and capacitive couplings between Josephson junctions have been taken into account in the calculations. The current-voltage characteristics, as well as time evolution of the spatial distribution of the electric charge in superconducting layers and the magnetic field, have been calculated in all Josephson junctions of the system. The coexistence of the longitudinal plasma wave and fluxon states has been observed in the region of parametric resonance beginning with a certain length of the Josephson junction. This indicates the appearance of a new unique collective excitation in the system of coupled Josephson junctions, namely, a composite state of the Josephson current, electric field, and vortex magnetic field.

Manifestation of resonance-related chaos in coupled Josephson junctions

Abstract Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase–charge and charge–charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current–voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

Common features of a vortex structure in long exponentially shaped Josephson junctions and Josephson junctions with inhomogeneities

Abstract We study the vortex structure in three different models of the long Josephson junction: the exponentially shaped Josephson junction and the Josephson junctions with the resistor and the shunt inhomogeneities in the barrier layer. For these three models the critical curves “critical current–magnetic field” are numerically constructed. We develop the idea of the equivalence of the exponentially shaped Josephson junction and the rectangular junction with the distributed inhomogeneity and demonstrate that at some parameters of the shunt and the resistor inhomogeneities in the ends of the junction the corresponding critical curves are very close to the exponentially shaped one.

Modeling of LC-shunted intrinsic Josephson junctions in high-Tc superconductors

Resonance phenomena in a model of intrinsic Josephson junctions shunted by LC-elements (L-inductance, C-capacitance) are studied. The phase dynamics and IV-characteristics are investigated in detail when the Josephson frequency approaches the frequency of the resonance circuit. A realization of parametric resonance through the excitation of a longitudinal plasma wave, within the bias current interval corresponding to the resonance circuit branch, is demonstrated. It is found that the temporal dependence of the total voltage of the stack, and the voltage measured across the shunt capacitor, reflect the charging of superconducting layers, a phenomenon which might be useful as a means of detecting such charging experimentally. Thus, based on the voltage dynamics, a novel method for the determination of charging in the superconducting layers of coupled Josephson junctions is proposed. A demonstration and discussion of the influence of external electromagnetic radiation on the IV-characteristics and charge-time dependence is given. Over certain parameter ranges the radiation causes an interesting new type of temporal splitting in the charge-time oscillations within the superconducting layers.