Josephson Junction Model Research Articles

Branching in current–voltage characteristics of intrinsic Josephson junctions

We study branching in the current–voltage characteristics of the intrinsic Josephsonjunctions of high-temperature superconductors in the framework of the capacitivelycoupled Josephson junction model with diffusion current. A system of dynamical equationsfor the gauge-invariant phase differences between superconducting layers for a stack of tenintrinsic junctions has been numerically solved. We have obtained a total branchstructure in the current–voltage characteristics. We demonstrate the existence of a‘breakpoint region’ on the current–voltage characteristics and explain it as aresult of resonance between Josephson and plasma oscillations. The effect of theboundary conditions is investigated. The existence of two outermost branches andcorrespondingly two breakpoint regions for the periodic boundary conditions is shown. Onebranch, which is observed only at periodic boundary conditions, corresponds to thepropagating of the plasma mode. The second one corresponds to the situation whenthe charge oscillations on the superconducting layers are absent, excluding thebreakpoint. A time dependence of the charge oscillations at breakpoints is presented.

Spiking and Bursting in Josephson Junction

This brief reports spiking and bursting in numerical simulations of the resistive–capacitive–inductive shunted Josephson junction model. Regular spiking, intrinsic bursting, and fast spiking, which are usually seen in the mammalian neocortex, are observed in the junction dynamics under external dc bias. The junction voltage is amplitude and frequency modulated when forced by weaker sinusoidal forcing of frequency much lower than the junction resonant frequency. For stronger forcing, bursting is observed. The autonomous junction also shows bursting in the high inductive regime. Bifurcation scenarios of bursting are discussed for both autonomous and nonautonomous cases.

Statics and dynamics of Bose-Einstein condensates in double square well potentials

We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.

Equidistance of branch structure in capacitively coupled Josephson junctions model with diffusion current

Branch structure in current–voltage characteristics of intrinsic Josephson junctions of HTSC is studied in the framework of two models: capacitively coupled Josephson junctions (CCJJ) model and CCJJ model with diffusion current (CCJJ + DC). We investigate the coupling dependence of the branch’s slopes and demonstrate that the equidistance of the branch structure in CCJJ model is broken at enough small values of coupling parameter (at α ≪ 1). We show that the inclusion of diffusion in the tunneling current through intrinsic Josephson junctions might restore the equidistance of the branch structure. Change of the current–voltage characteristics in CCJJ + DC model under variation of the coupling and McCumber parameters and effect of boundary conditions on the branch structure is analyzed.

Smooth NdBa2Cu3O7−δ thin films and ramp Josephson junctions

We report on c-axis oriented NdBa2Cu3O7−δ (NBCO) superconducting thin films grown on SrTiO3 substrates using pulsed laser deposition. The transition temperature of these NBCO films was around 89.5 K and the root mean square (RMS) surface roughness for 150 nm thick films was 0.75 nm. Insulating layers of of PrBa2Cu3O7−δ/SrTiO3/PrBa2Cu3O7−δ grown on top of the NBCO superconducting films result in superconductor/insulator multilayers of about 400 nm in total thickness and an RMS surface roughness of 2.4 nm. Smooth ramps with angles of about 20° are patterned in the multilayers using a photoresist reflow process and Ar ion milling. 15-25 nm thick Ga-doped of PrBa2Cu3O7−δ barriers and NBCO counter electrodes are deposited on the ramp forming Josephson junctions. Current-voltage (I - V) curves of the obtained ramp Josephson junctions were studied at 4.2 K. Multiple Shapiro steps were observed when the junctions were irradiated at frequencies around 10 GHz. The amplitudes of these steps oscillate with microwave power in agreement with the resistively shunted Josephson junction (RSJ) model.

Collective Dynamics of Intrinsic Josephson Junctions in HTSC

The dynamics of a stack of intrinsic Josephson junctions (IJJ) in the high-Tc superconductors is theoretically investigated with both the quasineutrality breakdown effect and quasiparticle charge imbalance effect taken into account. The current-voltage characteristics (IVC) of IJJ are numerically calculated in the framework of capacitively coupled Josephson junctions model and charge imbalance model including set of differential equations for phase differences, kinetic equations and generalized Josephson relations. We obtain the branch structure in IVC and investigate it as a function of model parameters such as coupling constant, McCumber parameter and number of junctions in the stack. The dependence of branch slopes and branch endpoints on the coupling and disequilibrium parameters are found. We study the nonequilibrium effects created by current injection and show that the increase in the disequilibrium parameter changes essentially the character of IVC. The new features of the hysteresis behavior of IVC of IJJ are obtained.

Influence of coupling parameter on current–voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors

We study the current–voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors by numerical calculations and in framework of capacitively coupled Josephson junctions model we obtain the total number of branches. The influence of the coupling parameter α on the current–voltage characteristics at fixed parameter β (β2=1/βc, where βc is McCumber parameter) and the influence of α on β-dependence of the current–voltage characteristics are investigated. We obtain the α-dependence of the branch’s slopes and branch’s endpoints. The presented results show new features of the coupling effect on the scheme of hysteresis jumps in current–voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors.

Vortices and dissipation in a bilayer thin film superconductor

Vortex dynamics in a bilayer thin film superconductor are studied through a Josephson-coupled double layer XY model. A renormalization group analysis shows that there are three possible states associated with the relative phase of the layers: a free vortex phase, a logarithmically confined vortex-antivortex pair phase, and a linearly confined phase. The phases may be distinguished by measuring the resistance to counterflow current. For a geometry in which current is injected and removed from the two layers at the same edge by an ideal (dissipationless) lead, we argue that the three phases yield distinct behaviors: metallic conductivity in the free vortex phase, a power law I-V in the logarithmically confined phase, and true dissipationless superconductivity in the linearly confined phase. Numerical simulations of a resistively shunted Josephson junction model reveal size dependences for the resistance of this system that support these expectations.

Effects of Grain Boundaries on Microwave Surface Resistance of Superconducting Films

Microwave surface resistance of superconducting films with grain boundaries (GBs) is theoretically investigated as the functions of the critical current density J/sub cj/ at GB junctions and of the film thickness d. The two-fluid model is used for electrical current in the grains, whereas the Josephson-junction model is adopted for tunneling current across GBs. Theoretical expressions of the surface resistance R/sub sf/ are obtained not only for weakly coupled GBs with small J/sub cj/ but also for strongly coupled GBs with large J/sub cj/. The results show that R/sub sf/ nonmonotonically depends on the critical current density J/sub cj/ at GB junctions, and R/sub sf/ of superconductors with GBs can be smaller than the surface resistance for ideal homogeneous superconductors without GB. The R/sub sf/ is proportional to 1/d for thin films of d/spl Lt/d/sub cr/ and R/sub sf/ is independent of d for thick slabs of d/spl Gt/d/sub cr/, where the crossover thickness d/sub cr/ is much larger than 2/spl lambda/ (where /spl lambda/ is the London penetration depth) for weakly coupled GBs.

Microwave surface resistance of superconductors with grain boundaries

Microwave-field distribution, dissipation, and surface impedance are theoretically investigated for superconductors with laminar grain boundaries (GBs). In the present theory we adopt the two-fluid model for intragrain transport current in the grains, and the Josephson-junction model for intergrain tunneling current across GBs. Results show that the surface resistance ${R}_{s}$ nonmonotonically depends on the critical current density ${J}_{cj}$ at GB junctions, and ${R}_{s}$ for superconductors with GBs can be smaller than the surface resistance ${R}_{s0}$ for ideal homogeneous superconductors without GBs.

Microwave-induced thermal escape in Josephson junctions.

We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multivalued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.

Localized rotating-modes in capacitively coupled intrinsic Josephson junctions: Systematic study of branching structure and collective dynamical instability

A variety of the $I--V$ characteristics observed in a stack of intrinsic Josephson junctions is systematically explained in terms of the dynamics of the localized rotating mode in the discrete nonlinear systems. We clarify the effect of the capacitive coupling constant on the $I--V$ characteristics, using the capacitively coupled Josephson junction model. The branch structure in the $I--V$ characteristics changes from an assembly of equidistance branches to a single hysteresis-loop-like structure as the capacitive coupling constant increases. This behavior is in accordance with experiments. We predict that dynamical transitions between collective rotating states take place in the resistive state of a stack of intrinsic Josephson junctions in the strong capacitive coupling regime. These transitions create step-like structure in the $I--V$ characteristics, which is observed in ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4\ensuremath{-}\ensuremath{\delta}}$.

Slow-fast dynamics in Josephson junctions

We report on a nontrivial type of slow-fast dynamics in a Josephson junction model externally shunted by a resistor and an inductor. For large values of the shunt inductance the slow manifold is highly folded, and different types of dynamical behavior in the fast variable are possible in dependence on the other parameters of the junction. We discuss how particular features of the dynamics are manifested in the current-voltage characteristics of the shunted junction.

Rf-induced dc voltages across unbiased terminals and current–voltage characteristics of microwave-driven high-Tc SQUIDs

Quantized voltage across the unbiased terminals of a bicrystal YBa2Cu3O7 dc SQUID exposed to microwave radiation has been observed at 77 K. Using this voltage as an indication of the microwave power coupled to the junctions, we identified three distinct regions in the I–V curves as the microwave power was tuned, similar to those reported for low-Tc SQUID. Pronounced double period steps were observed when the microwave radiation power was high enough to suppress the dc Josephson current completely. Half-integer steps also appeared as the applied dc-magnetic flux was close to half-integers of flux quanta. The experimental phenomenon was explained based on the resistively shunted Josephson junction model.

Grain-boundary dissipation in high-T c superconductors

Thin-film and bulk [001] tilt bicrystal grain boundaries (GBs) in YBa 2Cu 3O 7 exhibit a strong dependence of critical current density, J c, on misorientation angle. What was initially difficult to understand was the 30x smaller J c in bulk GBs which are microscopically more perfect. We review an explanation of this zero-field data, which is based on the pinning of Josephson vortices by the meandering found in thin-film GBs. In addition, there is evidence that J c of GBs does not drop as quickly with applied magnetic field as expected by simple Josephson junction models. The long-wavelength pinning potential due to meandering is less effective at high fields, but Gurevich and Cooley (GC) proposed a new mechanism for an enhanced GB J c arising from pinned Abrikosov vortices in the banks of a GB which present a static, quasiperiodic pinning potential to pin GB vortices. We fine a peak in J c and an unusual hysteresis which give considerable support to the GC concept. In low fields, the GBs exhibit a larger J c for field cooling, which is opposite to the usual hysteresis but agrees with GC due to the larger Abrikosov vortex density in the banks. Magnetization data on the same sample are consistent including the identification of the irreversibility field.

Efficient calculation of the current–voltage characteristic of a resistively shunted Josephson junction

We describe a method for calculating the current–voltage characteristics given by the resistively shunted Josephson junction model. The method is based on a continued fraction, and allows rapid calculation of the characteristic for arbitrary temperatures, in the low-capacitance regime.

Frequency characteristics of multiple Josephson junctions

We numerically analyze the multiple Josephson junction (MJJ) model of high T C superconductors. MJJ applied a constant current has many hysteresis branches in I– V characteristics and generates oscillating voltage. We find that the hysteresis branches are originated from various modes of rotating phase differences between superconducting layers, and that the frequency characteristics depend on rotational velocity of each phase. In MJJ applied an alternating current we also show harmonizations of spontaneous and external oscillations.

Interlayer dissipation in magnetic fields for H∥ J in κ-(ET) 2I 3

In this paper, we report transport measurements of the interlayer magnetoresistance with field, H, parallel to the current, J, in the organic superconductor κ-(bis(ethylenedithio)-tetrathiafulvalene (ET)) 2I 3. The isothermal magnetoresistance R( H) displays a peak as a function of field for 1> T/ T c≥0.4. At lower temperatures T/ T c<0.4, R( H) increases monotonically with field. Comparison with several other organic superconductors suggests the interlayer magnetoresistance peak is intrinsic to layered systems. Quantitative analysis shows that the magnetoresistance at small field can be fitted to the stacked Josephson-junction model with the normalized coupling energy proportional to (1− T/ T c) 3/2/ H.

Control of chaotic patterns in a Josephson junction model

The effect of an applied rf signal on the dynamics of a large-area Josephson junction is examined. The problem of controlling spatiotemporal chaotic patterns induced by the external magnetic field is addressed. Chaos control is conducted by a weak spatially distributed force.

Voltage-biasedI−Vcharacteristics in the multiple Josephson junction model of high-Tcsuperconductors

By use of the multiple Josephson junction model, we investigate voltage-biased I-$V$ characteristics by numerical simulation. We show that there exist three characteristic regions in the $I\ensuremath{-}V$ curve. In the low voltage region, the total current is periodic with trigonometric functional increases and rapid drops. Then a kind of chaotic region follows. Above a certain voltage, the total current behaves with a simple harmonic oscillation and the I-$V$ characteristics form a multiple branch structure as in the current-biased case.