Swihart Velocity Research Articles

Dynamics of fluxons in narrow window junctions

We numerically investigate the dynamics of a long window junction under the influence of a constant current bias, and intermediate damping in the junction area. The current voltage characteristics are calculated for various sizes of the passive region extension w′ and different thickness of the isolating layer in the idle region. The existence of the idle region influences the fluxon solutions, and consequently the I–V characteristics, causing the fluxons to increase their critical velocity above the Swihart velocity in the window and to radiate by way of the Cherenkov effect as they move in the junction. The fluxons become phase locked with the Cherenkov radiation, and this is reflected in the I–V curve as very strong resonances at relatively high velocities.

Electromagnetic properties andHe+irradiation effects onYBa2Cu3O7−xgrain-boundary Josephson junctions

We have analyzed the electromagnetic properties of small and long YBa2Cu3O7-x grain-boundary Josephson junctions. The Swihart velocity increases with junction width (rv) while the ratio of the relative dielectric constant to the barrier thickness (epsilon/t) decreases. We found that the product wX epsilon/t is approximately constant. These results have been explained in the framework of the filamentary model, where the barrier can be regarded as a disordered dielectric medium with a high density of superconducting filaments. Experiments demonstrate that a controllable variation of these parameters can be achieved by helium irradiation at 80 keV. We give examples of an enhancement of weak-link properties of junctions for doses in the range of 10(13) cm(-2) Raising the dose we can sweep the modification of the weak-link properties from an increase of the junction critical current of about 10% to a severe degradation of the coupling energy of the barrier, although the superconducting properties of the electrodes always worsen gradually.

About 4 π-kink in a Josephson junction

The first analytical description of the 4 π-kink Josephson vortex is presented for the model of the long Josephson junction with the sine-nonlinearity. The weakly nonlocal approach is used. This approach is efficient for the description of the vortices moving with the velocities which are close to the Swihart velocity. This new analytical result is obtained in the limit when the Josephson critical current density is not high enough.

Shape of a moving fluxon in stacked Josephson junctions

We study numerically and analytically the shape of a single fluxon moving in double stacked Josephson junctions (SJJ's) for various junction parameters. We show that the fluxon in a double SJJ 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. An analytic expression for the wavelength of Cherenkov radiation is derived.

Single fluxon in double-stacked Josephson junctions: Approximate analytic solution

We derive an approximate analytic solution for a single fluxon in a double stacked Josephson junctions (SJJ's) for arbitrary junction parameters and coupling strengths. It is shown that the fluxon in a double SJJ's can be characterized by two components, with different Swihart velocities and Josephson penetration depths. Using the perturbation theory we find the second order correction to the solution and analyze its accuracy. Comparison with direct numerical simulations shows a quantitative agreement between exact and approximate analytic solutions. It is shown that due to the presence of two components, 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.

Strong coupling effects in(Nb−Al−AlOx)2-Nb stacked Josephson junctions

Stacked $({\mathrm{N}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{l}\ensuremath{-}\mathrm{A}\mathrm{l}\mathrm{O}}_{x}{)}_{2}$-Nb long Josephson junctions with very thin intermediate Nb-Al superconducting layer are investigated experimentally and theoretically. Stable coherent in-phase zero-field steps (ZFS's) are observed; both the critical current and the maximum ZFS current dependence on magnetic field are measured to prove the in-phase nature of this mode. The dependences are in good agreement with the inductive coupling model. The Swihart velocities for in-phase $({c}_{+})$ and antiphase $({c}_{\ensuremath{-}})$ modes are measured for different lengths of the stacks. In order to make a proper interpretation of the experimental results, an extension of the existing model is developed, taking into account the fact that the middle electrode consists of two different superconductors (Nb and proximized Al). A comparison of a new model with the conventional model and experimental data is made. The extended model gives the ${c}_{+}/{c}_{\ensuremath{-}}$ ratio as 30% different from what the conventional model predicts. For thin Nb and Al layers the correction factor depends only on the ratio of the magnetic field penetration depths in Nb and proximized Al.

Microwave dynamics and electromagnetic properties of YBa 2Cu 3O 7 step-edge junctions on MgO substrates

In this paper, we report the successful fabrication and current-voltage characteristics of the epitaxial c-axis YBa 2Cu 3O 7 step-edge junctions (SEJs) on MgO substrates. The junctions were fabricated by patterning the laser deposited YBa 2Cu 3O 7 thin films on MgO substrates with ionmilled steps. Integer Shapiro steps were observed in the current-voltage characteristics up to 1 THz under 72 GHz external microwave irradiation. Additional subharmonic Shapiro steps have also been found in some junctions with small step height and film thickness ratio, which may be explained by the inhomogeneous YBa 2Cu 3O 7 grain boundary interface formed at the edges of the substrate step. Self-induced electromagnetic resonance (Fiske mode) peaks have been observed in the current-voltage curves of the SEJs with large step height and film thickness ratios. The Swihart velocity and the effective shunting capacitance have been estimated to be 6.9 × 10 6 m s −1 and 55 fF μm −2 at 4.2 K, respectively, from the voltage of the observed Fiske resonance. The shunting capacitance obtained from the electromagnetic resonance compares well with that estimated from the McCumber constant β c .

Static and dynamic properties of stacked Josephson junctions: Analytic solution

Static and dynamic properties of stacked Josephson junctions are studied theoretically. An approximate analytic solution for a stack with arbitrary junction parameters was obtained. The analytic solution is in good agreement with numerical simulations. Characteristic penetration depths, Swihart velocities, the lower critical field, the first integral, and the free energy for a stack of nonidentical junctions were derived and studied for different parameters of the stack. We show that attractive interaction of fluxons in adjacent junctions exists in the dynamic state of the stack, leading to appearance of the ``in-phase'' state with fluxons on top of each other. In a given external magnetic field the Gibbs free energy has a number of local minima corresponding to particular fluxon distributions (modes) in the stack each representing a quasiequilibrium state. For a stack of $N$ junctions each mode would result in $N$ distinct flux-flow branches in the current-voltage characteristic. Taking into account that different modes with equal total number of fluxons are not identical we conclude that the total possible number of flux-flow branches can be much larger than the number of junctions in the stack.

Slow electromagnetic waves in asymmetric SISIS′ junctions

Splitting of the Swihart velocity in the asymmetric SISIS′ devices (where S is a superconductor and I is an insulator) has been investigated. Analysis based on the existing models of the dynamic state of the stacked junctions shows that if one of the external electrodes, S′, has a considerably lower critical temperature T′ c than the other two electrodes, and the temperature of the system approaches T′ c but T< T′ c, then the velocities c + and c − approach their limit values: c + → c 0, and c − → 0 (here c 0 is the Swihart velocity in the single SIS junction). Experimentally, both asymmetric Nb/AlAlO x Nb/AlAlO x Ta/Nb and symmetric Nb/AlAlO x Nb/AlAlO x Nb two-terminal devices have been investigated. The values c − = (1.47 ± 0.04) × 10 6 m/s and c − = (1.7 ± 0.1) × 10 6 m/s have been obtained for the devices of the first and second type, respectively. Although, as expected, the value of c − is lower in the first case, the difference between the c − values for the two types of devices is rather small. This is in agreement with the theory, because in the first case the influence of the thickness of the middle electrode on the value of c − predominates the same effect arising from the reduced superconductivity of the Ta/Nb electrode.

Collective motion of Josephson vortices in intrinsic Josephson junctions inBi2Sr2CaCu2O8+y

We report on the experimental observation of moving Josephson vortices in mesa structures patterned on the surface of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{y}}$ single crystals. Mesas form stacks of typically 100 intrinsic Josephson junctions. In magnetic fields parallel to the superconducting copper oxide layers, a flux-flow branch develops on the current-voltage (I-V) characteristic. We investigate this branch in magnetic fields H up to 15 kOe for junctions with lateral dimensions ranging from 20\ifmmode\times\else\texttimes\fi{}20 \ensuremath{\mu}${\mathrm{m}}^{2}$ to 500\ifmmode\times\else\texttimes\fi{}20 \ensuremath{\mu}${\mathrm{m}}^{2}$. Investigations show that the voltage of the branch scales with 1/H. For mesas of the same height its slope is inversely proportional to the junction area showing that the flux-flow resistance is independent of the particular junction length. Microwave emission is sensitive to the direction of fluxon motion. This shows that the flux-flow branch in the I-V characteristic is caused by the collective motion of vortices. We compare our data to numerical simulations based on the coupled sine-Gordon equations for strongly coupled, stacked Josephson junctions. We show that the observed branch can be understood as a flux-flow state caused by vortices moving with the lowest collective-mode velocity of the system. The value derived for the Swihart velocity is in good agreement with recent measurements of the c-axis Josephson plasma frequency.

La1.85Sr0.15CuO4−δ bicrystal grain boundary Josephson junctions

We have investigated La1.85Sr0.15CuO4−δ grain boundary Josephson junctions (GBJs) fabricated on [001] tilt SrTiO3 bicrystals with misorientation angles of 24° and 36.8°. The resistive transition and the current–voltage characteristics of the GBJs are found to be close to those predicted by the resistively shunted junction (RSJ) model. Their product of the critical current density, Jc, and the normal resistance times area ρn, scales proportional to about (Jc)q with q=0.5–0.6 similar to what is found for YBa2Cu3O7−δ GBJs. By analyzing Fiske resonances the Swihart velocity of the GBJs and the ab-plane London penetration depth of La1.85Sr0.15CuO4−δ are obtained to c̄=2.5×106 m/s and λL=200 nm at 4.2 K, respectively.

On the solitary waves in the sine-Gordon model of the two-dimensional Josephson junction

The properties of the possible solitary electromagnetic waves, propagating in two-dimensional SIS Josephson junction without dissipative losses are investigated on the basis of the local theory of the junction. A classification of the waves in the junction with respect to the Swihart velocity is made. It is shown that allowed and forbidden areas for the wave numbers, wave frequency and wave amplitude exist. The cut-off frequency for the solitary waves which velocity is greater than the Swihart velocity can be smaller than the Josephson plasma frequency and moreover these waves can propagate only in a junction that is large in the direction perpendicular to the propagation direction. On the contrary the solitary waves which velocity is smaller than the Swihart velocity request junction size in the above direction to be smaller than a critical one. The investigated two-dimensional solitary waves can be connected with one or two quanta of the magnetic flux.

Two-fold stacks of long Josephson junctions with different parameters

The properties of the two-layer magnetically coupled long Josephson junction stacks are investigated theoretically. An expression for the Swihart velocities\(\bar c_ + \) and\(\bar c_ - \) is given for the case of different junction parameters. It is predicted that for asymmetric stack the first critical fieldH c1 is represented by two valuesH ↑ c1 andH ↓ c1 different from the fieldsH A c1 andH B c1 that characterize separate junctions. A calculation of the first critical fieldH ↑ c1 as a function of the junction parameters is made for the case of small difference in effective magnetic field penetration depths of the junctions.

Cavity modes in Josephson coupled superconductor/insulator superlattices

Cavity modes in Josephson coupled superconductor/insulator superlattices have been studied based on a theoretical model recently proposed by Sakai et al. In such systems the Swihart velocities form a band bounded by two limiting velocities c + and c − corresponding to the in-phase and out-of-phase (in the two neighboring junctions) states, respectively. Cavity modes in stacked double Josephson junctions have also been discussed as a special case.

Investigation on the properties and the applications of vertically stacked Josephson tunnel junctions

High quality vertically stacked Josephson tunnel junctions have been experimentally studied in the light of their potential applications. They have been realized using a simple fabrication process based on Nb technology. A number of aspects of such new devices were investigated. Among other things, we report on the dc characteristics (and their temperature and magnetic field dependence) of vertical stacks with particular attention to the case in which the intermediate layers are very thin. Furthermore, the Swihart velocities of the electromagnetic waves propagating in double-barrier junctions were measured from the voltages of zero field steps, Fiske steps, and flux flow steps in the current-voltage curve of electrically long devices. Each section is discussed in the light of the potential applications of vertically stacked junctions. We interpret the main features of the phenomena observed experimentally in terms of basic mechanisms. Strong evidence has been found of the proximity effect in thin intermediate layers. Vertically stacked Josephson tunnel junctions seem to be good candidates for applications as particle and photon detectors and high frequency oscillators.

Fabrication and superconducting transport properties of bicrystal grain boundary Josephson junctions on different substrates

We have reproducibly fabricated YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// (YBCO) grain boundary Josephson junctions (GBJs) on SrTiO/sub 3/ and MgO bicrystals as well as by introducing buffer layers between the c-axis oriented YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// film and the SrTiO/sub 3/ bicrystal substrate. For the additional layers non-superconducting Nd/sub 1.85/Ce/sub 0.15/CuO/sub x/ (NCCO) and NdGaO/sub 3/ were used. The effect of the layer structure on the superconducting transport properties of the GBJs was analyzed by measuring the current-voltage characteristics (IVCs), their derivatives, the resistive transition R(T), and the magnetic field dependence of the critical current I/sub c/(B). YBCO-GBJs fabricated on MgO and SrTiO/sub 3/ bicrystal substrates were found to have very similar low frequency characteristics. Fiske resonances were investigated to obtain information on the high-frequency properties. The Swihart velocity was found to be considerably smaller for GBJs fabricated on SrTiO/sub 3/ as compared to MgO due to the large relative dielectric constant of SrTiO/sub 3/ and the related stray capacitance. >

Josephson effect and single-particle tunneling in YBa 2Cu 3O 7− x and YbBa 2Cu 3O 7− x single-crystal break junctions

We have studied the current-voltage characteristics of break junctions in single crystals of YBa 2Cu 3O 7− x and YbBa 2Cu 3O 7− x at helium temperature. For a YBa 2Cu 3O 7− x Josephson junction Fiske resonances in low magnetic fields have been observed in the I( V) characteristics, thus proving the tunneling nature of the contact. The reduced velocity of the electromagnetic wave in the contact area has been calculated to be c/ c 0 ∼ 0.018 ( c is the Swihart velocity). The ratio of the barrier thickness d 1 to the relative dielectric constant of the barrier ϵ was found to be d I / ϵ ∼ 0.09 nm. In the quasiparticle tunneling regime, the YbBa 2Cu 3O 7− x break junctions showed in some cases I( V) characteristics with a relatively small excess current at “sub-gap” voltages and a steep rise of the current at the “gap” voltage V g = 2 Δ/ e. The “BCS-like” form of the observed I( V) characteristics seems to be in favor of s wave superconductivity.

New class of running-wave solutions of the (2+1)-dimensional sine-Gordon equation

A new class of running-wave solutions of the (2+1)-dimensional sine-Gordon equation is investigated. The obtained waves require two spatial dimensions for their propagation, i.e. they generalize solutions of the (2+0)-dimensional sine-Gordon equation. The parameters of the waves strongly depend on the wave amplitude and there exist forbidden areas for the wavenumber and frequency. The obtained solutions describe a new class of Josephson waves whose velocity is smaller than the Swihart velocity. If omega =0 the running waves are reduced to the self-consistent phase, current and magnetic field distributions in a large two-dimensional Josephson junction. The self-restriction coefficient for the Josephson current corresponding to one of the structures is calculated.

Nb/Al/AlOx/Nb stacked long Josephson junctions

We have fabricated and tested Josephson tunneling structures made of two stacked Nb/Al/AlOx/Nb long junctions in which the thickness of the intermediate electrode is less than λ L . We report the observation of two phenomena: a considerable decrease of the Swihart velocity and a small but finite voltage jump of the quasiparticle voltage of one junction whenever the other one switches from the superconducting state to the normal state or between dynamical states.

Stimulated waves of electric and magnetic fields in a two-dimensional semi-infinite Josephson junction

A two-dimensional semi-infinite Josephson junction without damping is considered. Its interaction with an external oscillating electromagnetic field in the form of a running wave with a phase velocity equal to the Swihart velocity is investigated. The results obtained are based on an exact solution of the (2+1)-dimensional sine-Gordon equation, depending on an arbitrary function. The boundary conditions on the interface are provided by an external time-varying electric field consistent with the exact solution. Under these conditions, an electromagnetic structure arises inside the junction. It is shown how the existence of this formation may be proved experimentally. A method for measuring the Swihart velocity is proposed.