Two-dimensional Josephson Junction Research Articles

Radiation emission due to fluxon scattering on an inhomogeneity in a large two-dimensional Josephson junction

Interaction of a fluxon in the two-dimensional large Josephson junction with the finite area inhomogeneity is studied within the sine-Gordon theory. The spectral density of the emitted plane waves is computed exactly for the rectangular and rhombic inhomogeneities. Total emitted energy as a function of the fluxon velocity exhibits at least one local maximum. Connection to the previously studied limiting cases including the point impurity and the one-dimensional limit has been performed. An important feature o f the emitted energy as a function of the fluxon velocity is a clear maximum (or maxima). The dependence of these maxima on the geometric properties of the impurity has been studied in detail.

Radiation in the process of fluxon interaction with a rectangular impurity in two-dimensional Josephson junction

The Josephson vortex (fluxon) interaction with the rectangular impurity of finite size in two-dimensional Josephson junction with dissipation is studied. The energy density radiated during the scattering of fluxon on inhomogeneity is found. The total radiation energy dependence as a function of the fluxon velocity and impurity size is obtained. The dependence has a resonant behavior that can be explaned by the interference of emitted waves. Keywords: fluxon, microshort, Josephson junction, sine-Gordon equation.

Berezinskii–Kosterlitz–Thouless transition in two-dimensional arrays of Josephson coupled Bose–Einstein condensates

Abstract We study the phase transition occurring in Bose–Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii–Kosterlitz–Thouless transition at a finite temperature T KT to the ordered state composed of bound vortex–antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature T KT . Finally, we discuss the results in the context of system parameters and possible experiments.

Fluxon Scattering on a Stripe-Like Impurity in a Two-Dimensional Josephson Junction

The interaction of a soliton (fluxon) with a stripe-like inhomogeneity in a two-dimensional Josephson junction is studied. The radiation emitted due to the fluxon scattering on the impurity is calculated. The total radiation energy shows a distinct resonant dependence as a function of the fluxon velocity. The current-voltage characteristic of such a junction with a fluxon trapped in it is calculated. The signature of the emitted radiation on the current-voltage dependence is analyzed.

Vortex dynamics in two-dimensional Josephson junction arrays with asymmetrically bimodulated potential

On the basis of resistively-shunted junction dynamics, we study vortex dynamics in two-dimensional Josephson junction arrays with asymmetrically single and bimodulated periodic pinning potential for the full range of vortex density f. The ratchet effect occurring at a certain range of temperature, current, and f, is observed in our simulation. We explain the microscopic behavior behind this effect by analyzing the vortex distribution and interaction. The reversal of the ratchet effect can be observed at several f values for a small driven current. This effect is stronger when the asymmetric potential is simultaneously introduced in two directions.

Simulated radiation effects in the superinsulating phase of titanium nitride films

This paper investigates possible effects of alpha particle and ion beam irradiation on the properties of the superinsulating phase, recently observed in titanium nitride films, by using numerical simulation of particle transport. Unique physical properties of the superinsulating state are considered by relying on a two-dimensional Josephson junction array as a model of material structure. It is suggested that radiation-induced change of the Josephson junction charging energy would not affect the current-voltage characteristics of the superinsulating film significantly. However, it is theorized that a relapse to an insulating state with thermally activated resistance is possible, due to radiation-induced disruption of the fine-tuned granular structure. The breaking of Cooper pairs caused by incident and displaced ions may also destroy the conditions for a superinsulating phase to exist. Finally, even the energy loss to phonons can influence the superinsulating state, by increasing the effective temperature of the phonon thermostat, thereby reestablishing means for an energy exchange that can support Cooper pair tunneling.

Existence and stability analysis of semifluxons in disk-shaped two-dimensional0−πJosephson junctions

We consider a disk-shaped two-dimensional Josephson junction with concentric regions of 0- and $\ensuremath{\pi}$-phase shifts and investigate its ground states. This system is described by a $(2+1)$-dimensional sine-Gordon equation, which becomes effectively one dimensional in polar coordinates when one considers radially symmetric static solutions. We show that there is a parameter region in which the ground state corresponds to a spontaneously created ring-shaped semifluxon. We use a Hamiltonian energy characterization to describe analytically the dependence of the semifluxonlike ground state on the junction size and the applied bias current. We present numerical calculations to support our analytical results. We also discuss the existence and stability of excited states bifurcating from a uniform solution.

Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the(2+1)-dimensional sine-Gordon model

We predict a class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line of an arbitrary profile. We derive a universal analytical expression for the energy of arbitrary-shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically-moving Josephson vortex and suggest an experiment to measure a time-dilation effect analogous to that in special relativity. The position of the shape excitation on a Josephson vortex acts like a ``minute hand'' showing the time in the rest frame associated with the vortex. Remarkably, at some conditions, the shape wave can carry negative energy: a vortex with the shape excitation can have less energy than the same vortex without it.

Phase transitions in Josephson junction arrays in a weak magnetic field

Based on the resistively shunted junction dynamics, we numerically investigate the superconducting phase transitions of two-dimensional Josephson junction arrays exposed to a dilute external field with the magnetic flux density f=1/25. Dynamic scaling analysis of current-voltage characteristics shows that a Kosterlitz–Thouless–Berezinskii (KTB) phase transition occurs at a finite temperature in the absence of disorder. When the disorder is introduced into the bond, the phase transition would be driven into a non-KTB type, where a possible glass transition is suggested. The effects of the bond disorder on the critical temperature and critical exponents are also discussed. The further experimental works to realize well known KTB and glass transitions in Josephson junction arrays are clearly called for.

Phase transition in site-diluted Josephson junction arrays: A numerical study

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied; evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings but also shed some light on the relevant phase transitions.

Uniformly frustrated Josephson junction array in trapped Bose-Einstein condensates

We investigate the ground state structure of two-dimensional Josephson junction arrays consisting of Bose-Einstein condensates trapped by both a rotating harmonic potential and a corotating deep optical lattice with square symmetry. Monte Carlo simulations of the uniformly frustrated XY model in a wide range of the frustration parameter f reveal that the stable configuration of vortices for a simple fractional number f is a staircase structure, consisting of diagonal chains of vortices with periodic lattice of unit cells.

Magnetic-field-induced phase transition of vortex glass states in disordered Josephson junction arrays

Using the resistively shunted junction model，we study magnetic-field-induced phase transitions of the vortex glass states in a disordered two-dimensional Josephson junction array. From calculated results of the vorticity of the vortex system and the voltage noise generated by current-driven vortices as a function of the magnetic field， the following conclusions can be drawn. 1） With decreasing the magnetic field， the vortex system exhibits a reentrant transition from a vortex glass phase to a pinned dilute vortex liquid. 2） There is a peak of voltage noise driven by the current in the vortex glass state. It follows that the system is in a sub-stable state as a result of the competition between ordered and disordered interactions， which results in peak effects of the critical current. The calculated results are consistent with recent experimental reports by Okuma and Kamada on disordered and superconducting MoxSi1-x films.

Shape Waves in 2D Josephson Junctions: Exact Solutions and Time Dilation

We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.

Dissipation-Driven Quantum Phase Transition in Superconductor-Graphene Systems

We show that a system of Josephson junctions coupled via low-resistance tunneling contacts to graphene substrate(s) may effectively operate as a current switching device. The effect is based on the dissipation-driven superconductor-to-insulator quantum phase transition, which happens due to the interplay of the Josephson effect and Coulomb blockade. Coupling to a graphene substrate with gapless excitations further enhances charge fluctuations favoring superconductivity. The effect is shown to scale exponentially with the Fermi energy in graphene, which can be controlled by the gate voltage. We develop a theory that quantitatively describes the quantum phase transition in a two-dimensional Josephson junction array, but it is expected to provide a reliable qualitative description for one-dimensional systems as well.

Depinning and creep in Josephson junction arrays in weak magnetic fields

Based on resistively shunted junction dynamics, we have numerically studied the depinning transition and thermally activated creep motion of vortices in two-dimensional Josephson junction arrays exposed to a weak external field with the filling factor $f=1/25$. Whether the bond disorder is introduced into the system or not, a continuous depinning transition is found at zero temperature. By means of scaling analysis of the current-voltage characteristics, a non-Arrhenius creep law is observed at finite temperatures, with the existence of two universality classes depending on the strength of the bond disorder. The effects of the disorder on the critical current and critical exponents are also discussed.

Vortex Lattices in Rotating Bose-Einstein Condensate in an Optical Lattice: Analogy to Uniformly Frustrated Josephson-Junction Arrays

We investigate the effect of rotation for two-dimensional Josephson junction arrays consisting of atomic Bose-Einstein condensates trapped by both a harmonic trap and an optical lattice. This system is analogous to the superconducting Josephson junction array to which a transverse magnetic field is applied, being described by the uniformly frustrated XY model. The frustration parameter f, defined by the rotation frequency of the condensate and the lattice constant of the optical lattice, is an important parameter to determine the ground state. The numerical simulations of the Gross-Pitaevskii equation reveal that for f=1/2 the ground state possesses the checkerboard pattern of vortices, and for f<1/2 the vortex configuration is characterized by the staircase form.

Thermal propagation of fluxons in two-dimensional Josephson junction arrays

We have modeled flux quanta propagation in two-dimensional square arrays of small Josephson junctions when the motion is hampered by the presence of an effective barrier due to the superconducting loops. The energy barriers have been estimated simulating the effect of thermal fluctuations and evaluating the barrier via the Arrhenius factor. The results have been compared with a much simpler semianalytic method, showing that the method is able to give an acceptable estimate. The strength of the fluxon-(anti)fluxon interaction as a function of the loop inductance and the distance between the excitations has been also evaluated. It is reported that the presence of a finite inductance substantially affects the interaction potential, and the contributions due to mutual inductances are found to further change the behavior of the interaction.

Non-equilibriumPhase Transition of Two-dimensional Fully-frustrated Josephson Junction Arrays

Non-equilibriumPhase Transition of Two-dimensional Fully-frustrated Josephson Junction Arrays

Phase transition and vortex noise spectrum in two-dimensional Josephson-junction array

Using the resistively shunted junction (RSJ) model，we calculate the temperature dependence of vorticities and fluctuations of vorticities in two-dimensional Josephson junction array (JJA). It is found that the phase transition is of the Berezinski-Kosterlitz-Thouless (KTB) type. We also study the temperature and driving current dependence of the noise power spectrum in the vicinity of phase transition. The calculated results are consistent with recent experimental reports, and the main characteristics of the noise power spectrum can be explained by the motion of vortices.

Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder

We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of ${E}_{J}∕{k}_{B}$ with the Josephson coupling strength ${E}_{J}$), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.