Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

Resistance oscillations in junctions of superconductor–magnetic system

Resistance oscillations as a function of magnetic field were observed in superconductor–magnetic tunnel junctions of Nb–Fe–FeO_x–SiO₂–Au–Nb. Junctions involving superconductor–magnetic layer superconductor system are exciting because for certain regime of ferromagnetic layer thickness, a Josephson coupling with an intrinsic phase difference of π might be stabilized. For fabrication of the tunnel junctions the thin films were deposited by RF/DC magnetron sputtering. Using photolithography and reactive ion etching, square junctions of size varying from 50 μm to 250 μm were defined. I–V characteristics and R vs. H characteristics were studied at 4.2 K. When the magnetic field is applied parallel to the junction plane, measurements of the junction resistance as a function of magnetic field at a fixed temperature show resistance peaks whenever the total magnetic flux through the junction equals an integral multiple of flux quantum. The penetration depth of the superconducting electrodes was estimated from the positions of the resistance peaks.     

Critical current calculations for long 0-π Josephson junctions

A zigzag boundary between a $d_{x^2 - y^2}$ and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J_c(H_a) is maximum at non-zero applied magnetic field H_a, and depends strongly on the ratio of Josephson penetration depth λ_J to facet length L_f. If λ_J/L_f ≫1 and the number of facets is large, there is a broad range of H_a where J_c(H_a) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ_J/L_f →∞, our model reduces to a previously-obtained analytical superposition result for J_c(H_a). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q_J(H_a), finding that . We suggest that measuring the field-dependence of Q_J(H_a) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.     

Manifestation of geometric resonance in current dependence of AC susceptibility for unshunted array of Nb–Alx–Nb Josephson junctions

A pronounced resonance-like structure has been observed in the current dependence of AC susceptibility for two-dimensional array of unshunted Nb–Al_x–Nb Josephson junctions. Using a single-plaquette approximation, we were able to successfully fit our data assuming that resonance structure is related to the geometric (inductive) properties of the array.     

Waiting times of entangled electrons in normal–superconducting junctions

We consider a normal–superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from splitting of Cooper pairs at the interface and demonstrate a significant enhancement of the probability to detect two consecutive electrons in a short time interval. Finally, we discuss the electronic waiting time distribution in the more realistic situation of partial entanglement.     

Reprint of : Waiting times of entangled electrons in normal–superconducting junctions

We consider a normal–superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from splitting of Cooper pairs at the interface and demonstrate a significant enhancement of the probability to detect two consecutive electrons in a short time interval. Finally, we discuss the electronic waiting time distribution in the more realistic situation of partial entanglement.     

Bulk—like contribution of tunnel magnetoresistance in magnetic tunnel junctions

We have demonstrated that the bulk-like contribution to tunnelling magnetoresistance (TMR) exists in the magnetic tunnel junctions, and is determined by the tunnelling characteristic length of the ferromagnetic electrodes. In the experiment, a wedge-shaped CoFe layer is inserted at the interface between the insulating barrier and the reference electrode. It is found that TMR ratio increases from 18% without CoFe layer to a saturation value of 26.5% when the CoFe thickness is about 2.3 nm. The tunnelling characteristic length, l_{tc}, can be obtained to be about 0.8 nm for CoFe materials.     

The formation of α at triple junctions of parent β phase in titanium alloys

We have examined the formation of α phase at grain boundary triple junctions of parent β in a metastable β titanium alloy with orientation imaging microscopy based on electron backscattered diffraction (EBSD). As in the case of α formed at grain boundaries of parent β grains, α at a triple junction also forms with the Burgers orientation relationship with one of the three neighbouring β grains. The experimental results are analyzed in terms of the deviation of the 36 possible α variants that can form at a triple junction from the Burgers orientation relationship with neighbouring grains.     

Vortex domain structures and dc currentdependence of magneto-resistances in magnetic tunnel junctions

Microfabrication and the magneto-transport characteristics of the magnetic tunnel junctions (MTJs) with a spin-valve-type structure of Ta (5nm)/Ni_{79}Fe_{21} (25nm)/Ir_{22}Mn_{78} (12nm)/Co_{75}Fe_{25} (4nm)/Al(0.8nm) oxide/Co_{75}Fe_{25} (4nm)/Ni_{79}Fe_{21} (20nm)/Ta(5nm) were investigated in this paper. A series of experimental data measured with a MTJ was used to verify a magnon-assisted tunnelling model and theory. Furthermore, a micromagnetics simulation shows that the butterfly-like vortex domain structures can be formed under a current-induced Oersted field, which decreases the net magnetization values of the ferromagnetic electrodes under a large dc current (i.e., in high voltage regimes). It is one of the main reasons for the tunnel magnetoresistance ratios to decrease significantly at high voltage biasing.     

Effect of inductive and capacitive coupling on the current–voltage characteristic and electromagnetic radiation from a system of Josephson junctions

We have studied the current–voltage characteristic of a system of long Josephson junctions taking into account the inductive and capacitive coupling. The dependence of the average time derivative of the phase difference on the bias current and spatiotemporal dependences of the phase difference and magnetic field in each junction are considered. The possibility of branching of the current–voltage characteristic in the region of zero field step, which is associated with different numbers of fluxons in individual Josephson junctions, is demonstrated. The current–voltage characteristic of the system of Josephson junctions is compared with the case of a single junction, and it is shown that the observed branching is due to coupling between the junctions. The intensity of electromagnetic radiation associated with motion of fluxons is calculated, and the effect of coupling between junctions on the radiation power is analyzed.     

Angular dependence of shot noise in the presence of Rashba spin–orbit coupling in semiconductor spintronics junctions

We investigate spin-dependent current and shot noise, taking into account the Rashba spin–orbit coupling (RSOC) effect in double diluted magnetic semiconductor (DMS) barrier resonant tunneling diodes. The calculation is based on an effective mass approach. The magnetization of DMS is calculated by the mean-field approximation in low magnetic field. The spin-splitting of DMS depends on the sp–d exchange interaction. We also examine the dependence of transport properties of CdTe/CdMnTe heterostructures on applied voltage and relative angle between the magnetization of two DMS layers. It is found that the RSOC has great different influence on the transport properties of tunneling electrons with spin-up and spin-down, which have different contributions to the current and the shot noise. Also, we can see that the RSOC enhances the spin polarization of the system, which makes the nanostructure a good candidate for new spin filter devices. Thus, these numerical results may shed light on the next applications of quantum multilayer systems and make them a good choice for future spintronics devices.     

The influences of the second harmonics together with the asymmetries of junctions on the voltage–current characteristics of high TC DC SQUIDs

We consider a superconducting quantum interference device having two arbitrary different over damped junctions transporting different currents. By replacing the governed two-dimensional Fokker–Planck equation with two one-dimensional equations, two density probability currents are appeared which determine the statistical average of the time-averaged total voltage across the device. To obtain the density probability currents, two coupled integral equations are introduced. These equations together with two other equations coming from normalizing conditions, found one generalized formulation for the voltage–current characteristics of the device. Based on that, the voltage–current characteristics of large inductance asymmetric DC SQUIDs having first and second harmonics in their current-phase relations are obtained and some predictions are illustrated.     

π-0 transition in superconductor-ferromagnet-superconductor junctions

Superconductor-ferromagnet-superconductor (SFS) Josephson junctions are known to exhibit a transition between π and 0 states. In this letter, we find the π-0 phase diagram of an SFS junction depending on the transparency of an intermediate insulating layer (I). We show that, in general, the Josephson critical current is nonzero at the π-0 transition temperature. Contributions to the current from the two spin channels nearly compensate each other, and the first harmonic of the Josephson current as a function of phase difference is suppressed. However, higher harmonics give a nonzero contribution to the supercurrent.     

Leakage current analysis of La0.67Sr0.33MnO3/Nb:SrTiO3 p–n junctions

La_0.67Sr_0.33MnO₃ (LSMO) films were grown on 0.7 wt% Nb-doped SrTiO₃ (NSTO) single-crystal substrates by pulsed laser deposition. The crystal phase structure and surface morphology of the LSMO films were investigated by means of X-ray diffraction method and atomic force microscopy, respectively. The diode-like behavior was observed in the leakage currents of the LSMO/NSTO heterojunction, by which I–V curves were measured at room temperature. The leakage current of LSMO/NSTO heterojunction follows the space-charge-limited conduction (SCLC) model under lower forward bias. As the forward bias increases, the barrier at the LSMO/NSTO interface becomes narrower and lower, which allows electrons to go over/through the interface barrier by the conduction mechanisms of Schottky emission and interface-limited Fowler–Nordheim tunneling, respectively. Under the same backward bias, the leakage current still undergoes the Ohmic law region according to the SCLC model, which is due to the drift currents of holes in the LSMO films and electrons in the NSTO substrates.     

Voltage–current characteristics and current instability conditions of a high-temperature superconductor in non-uniform temperature distribution

The influence of non-uniform temperature distribution in the cross section of a high-temperature superconductor (thermal size effect) on its voltage–current characteristic and the instability conditions of charged current is investigated. The boundary values of the electric field and the current above which the charged current is unstable are defined taking into account the size effect. It is shown that the calculated current of the instability determining the maximum allowable value of the charged current is reduced, if the thermal heterogeneity of the electrodynamics states is taken into consideration in the theoretical analysis of the stability conditions. As a result, the limiting stable values of the electric field and current depend nonlinearly on the thickness of the superconductor, its critical properties as well as on the external cooling conditions. Therefore, the current of instability will not increase proportionally to the increase in the thickness of superconductor or its critical current density at the intensive cooling conditions.     

Critical current density behaviors across a grain boundary inclined to current with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions

The critical current density behaviors across a bicrystal grain boundary(GB) inclined to the current direction with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions in magnetic fields are investigated.There are two main reasons for the difference in critical current density in junctions at different GB inclined angles in the same magnetic field:(i) the GB plane area determines the current carrying cross section;(ii) the vortex motion dynamics at the GB affects the critical current value when the vortex starts to move along the GB by Lorentz force.Furthermore,the vortex motion in a bicrystal GB is studied by investigating transverse(Hall) and longitudinal current–voltage characteristics(I–V_(xx) and I–V_(xy)).It is found that the I–V_(xx) curve diverges from linearity at a high driving current,while the I–V_(xy) curve keeps nearly linear,which indicates the vortices inside the GB break out of the GB by Lorentz force.     

Splitting of thin current sheets in the Earth’s magnetosphere

An analytic model of a one-dimensional self-consistent anisotropic thin current sheet is proposed. This model describes the sheet with a split (or bifurcated) structure, where the current density is minimal at the center and maximal at the edges. The model is specified by the set of Vlasov-Maxwell equations that reduces to the Grad-Shafranov equation. Under the assumption that particles move quasi-adiabatically, i.e., that the approximate integral of motion I_z is conserved, the slow evolution of the system in the course of diffusion of the distribution function in I_z is analyzed. Scattering processes can give rise to the partial capture of flying ions near the current sheet. Since the current of such quasi-trapped particles is directed oppositely to the current of flying particles, the local current at the center of the sheet is fully or partially compensated. As a result, the ordinary single-peak shape of the current density profile changes to the bifurcated shape. Such a structure is characteristic of the thin current sheet before the total destruction, when the tension of the magnetic field is unbalanced. Numerical calculations are corroborated by the observations of split current sheets in the magnetotail by the Cluster and Geotail satellites. The obtained results indicate that a possible mechanism of the destruction of the thin current sheet is not necessarily associated with the development of plasma instabilities but can be evolutionary.     

Dynamical current–current correlation in two-dimensional parabolic Dirac systems

We theoretically investigate the current–current correlation of the two-dimensional (2D) parabolic Dirac system in hexogonal lattice. The analytical expressions of the random phase approximation (RPA) susceptibility, Ruderman–Kittel–Kasuya–Yosida (RKKY) Hamiltonian, and the diamagnetic orbital susceptibility in noninteracting case base on the density–density or current–current correlation function are derived and quantitatively analyzed. In noninteracting case, the dynamical polarization within RPA, and spin transverse susceptibility as well as the RKKY interaction (when close to the half-filling) are related to the current–current response in the 2D parabolic Dirac systems. Both the cases of anisotropic dispersion and isotropic dispersion are discussed.