An asymptotic solution for the resistively shunted junction (RSJ) model of the Josephson junction

Using the method developed by Bogolyubov et al., we find analytically a steady-state solution for the resistively shunted junction (RSJ) model of the Josephson junction that is driven by a constant current source. This solution explains how the relative amplitude of the voltage oscillation depends on the junction parameters such as I ₀ (the critical current), R (the resistance), C (the capacitance), and the external current I _e . The validity of the analytical solution is assessed by comparing it with numerical results. We find that this solution is useful for normal tunnel junction with I _e /I ₀ of order 1 or larger, and for any other weak links with I _e /I ₀ much larger than 1.     

Comparative study of shunted bicrystal Josephson junctions

In order to optimize the series array performance of Y Ba₂Cu₃O_7−x (YBCO) grain boundary shunted junctions, a method to determine and control the junction resistance R_s and Au/YBCO contact resistivity ρ _c has been developed. 200 nm thick c-oriented YBCO films were grown by intermittent thermal coevaporation on bicrystal yttria-stabilized zirconia substrates. A gold contact overlayer of thickness d_n was deposited in situ. Normal junction resistances have been measured as a function of d_n and shunt width w. It was shown that, in accordance with theoretical estimates, the junction shunt resistance is essentially controlled by the c-axis Au/YBCO interface specific resistance and scales as . The product ρ _c ρ _n ≃ 3.10⁻¹⁴ Ω² cm ³ was estimated from the experimental data, leading to ρ _c ≈ 10⁻⁸ Ωcm ² for typical values of ρ _n for gold thin films.     

Josephson junction with an amorphous silicon barrier

A Josephson junction Nb/Si/Nb with a 10 nm thick amorphous silicon barrier is studied. The upper electrode contains a 2 nm thick sublayer of amorphous phase adjacent to the barrier, as revealed by cross-sectional TEM. Thus, the junction can be considered as a S-I-N-S system with the N layer represented by amorphous niobium. Peculiarities in the I–V and Δ(T) dependencies are observed and explained as a consequence of a proximity effect present in the upper electrode.     

Comparison between the resistively shunted Josephson junction model incorporating a voltage-dependent current-phase relation and experiments on superconducting thin-film microbridges

A voltage-dependent current-phase relation for short microbridges, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaaeysaWGaae4CaOGaaiikaiaabAfacaGGSaGaaeiiaiabgwGiglaa% cMcacaqGGaGaeyypa0JaaeiiaiaabMeamiaaicdakiaacIcacaqGwb% GaaiykaiaabccaciGGZbGaaiyAaiaac6gacaqGGaGaeyybIySaaeii% aiabgUcaRiaabccacaqGjbadcaaIXaGccaGGOaGaaeOvaiaabccaca% GGPaGaaeiiaiGacogacaGGVbGaai4CaiaabccacqGHfiIXcaqGGaGa% ey4kaSIaaeiiaiaabMeamiaaikdakiaacIcacaqGwbGaaiykaaaa!6017!\[{\rm{Is}}({\rm{V}},{\rm{ }}\emptyset ){\rm{ }} = {\rm{ I}}0({\rm{V}}){\rm{ }}\sin {\rm{ }}\emptyset {\rm{ }} + {\rm{ I}}1({\rm{V }}){\rm{ }}\cos {\rm{ }}\emptyset {\rm{ }} + {\rm{ I}}2({\rm{V}})\] is calculated on the basis of time-dependent Ginzburg—Landau theory. Used in the current-controlled resistively shunted Josephson junction model such a current-phase relation enables us to explain a number of features in the I–V characteristics of thin-film microbridges. Experimentally we can estimate the upper frequency limit of the Josephson effect in thin-film microbridges.     

2D Josephson junction

The paper is devoted to the determination of processes in the two-dimensional Josephson junction via numerical solution of 2+1 dimensional sine-Gordon equation (sGe) with suitably chosen boundary conditions. There is adopted an assumption that the normal derivative of the phase order parameter on a border of a junction is given by the surface current distribution on superconductive electrodes. This current distribution can be determined exactly since it makes a linear problem even in a presence of an external magnetic field although the surface current distribution is not uniform and can be singular. A rectangular junction is discussed as an example.     

Turn-on delay of a Josephson junction

An attempt has been made to give a new definition of turn-on delay of a Josephson junction which differs from earlier works. On the basis of our definition, an analytical expression of turn-on delay has been developed. This analytical model is based on a concept inherently different from those of Harris and McDonaldet al. It is observed that based on our model, the analytical expression of McDonaldet al. can also be obtained. A comparative study between our turn-on delay and those of Harris and McDonaldet al. is also made. It is expected that our definition and analytical expression of turn-on delay will eliminate the drawbacks and confusions of earlier investigations. The present work will find use in critically ascertaining the switching speed of Josephson analogs and digital circuits.     

Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction

Epitaxially grown, high quality semiconductor InSb nanowires are emerging material systems for the development of high performance nanoelectronics and quantum information processing and communication devices and for the studies of new physical phenomena in solid state systems. Here, we report on measurements of a superconductor-normal conductor-superconductor junction device fabricated from an InSb nanowire with aluminum-based superconducting contacts. The measurements show a proximity-induced supercurrent flowing through the InSb nanowire segment with a critical current tunable by a gate in the current bias configuration and multiple Andreev reflection characteristics in the voltage bias configuration. The temperature dependence and the magnetic field dependence of the critical current and the multiple Andreev reflection characteristics of the junction are also studied. Furthermore, we extract the excess current from the measurements and study its temperature and magnetic field dependences. The successful observation of the superconductivity in the InSb nanowire-based Josephson junction device indicates that InSb nanowires provide an excellent material system for creating and observing novel physical phenomena such as Majorana fermions in solid-state systems.     

Excitation of Josephson junction by an electromagnetic field in the nonlinear process formalism

The numerical analysis of the excitation of the Josephson junction (Jj) by an external electromagnetic field has been reported. The fully nonlinear approach requires using the quasiperiodic solutions of the sine-Gordon equation (sGe) which are expressed by the Riemann theta functions. Their local soliton approximation of the nondissipative Jj is presented. Using the self-consistent phenomenological model of a long Jj, the influence of the external electromagnetic field on the volt-ampere characteristics is considered.     

Ginzburg-Landau theory for three-dimensional Josephson junction arrays

We have derived a mean-field theory and a Ginzburg-Landau (GL) theory for classical three-dimensional Josephson junction arrays. We show that the full GL theory for arrays is formally equivalent to the GL theory for a bulk superconductor, demonstrating that for low fields and close to the critical temperature, the two systems are electrodynamically equivalent. We derive expressions for the penetration depth and coherence length, the effective superfluid density, critical fields, and the current-phase relationship for arrays. Using the Ginzburg criterion, we show that the critical region is very wide and that three-dimensional critical fluctuations should be experimentally accessible. Although the wide critical region casts doubt on the strict validity of the GL theory, suitable modifications of the coefficients should allow it to be used at lower temperatures, as is done for bulk superconductors.     

Magnetization and pinning effect of a Josephson junction

The magnetization and the pinning effect of a Josephson junction have been analyzed by using a mechanical analog. The influences of an applied current on the magnetization and the critical current have been studied. The peak and the training effects have been observed when inhomogeneities are introduced into the junction. The behavior of the junction is qualitatively analogous to that of a type II superconductor. The mechanical model is a useful analog computer for studying precisely and visually the vortex behavior of the junction and is also helpful in understanding qualitatively that of a type II superconductor.     

Simulation of Josephson junction in a microwave field

The resistively shunted junction (RSJ) model of a Josephson junction in a microwave field is studied using both analog and digital simulators. A comparison of the two methods shows very good agreement. Voltage-current characteristics of the Josephson junction in the low-frequency limit and their transition to chaotic behavior due to the punchthrough effect are investigated. The inverse ac effect on high- _c junctions is simulated. Fractional inverse steps are found.     

Phase transition of frustrated two-dimensional Josephson junction arrays

We have investigated the resistive behavior of frustrated Josephson tunnel junction arrays. The transitions nearf=1/2, atf=1 and at a nonspecial value off=0.38 are studied in detail with linear and nonlinear resistance measurements. The parameterf is the frustration index, the applied flux per unit cell of the array normalized to the flux quantum ₀=h/2e. The transition atf=1/2 looks similar to the zero-field Kosterlitz-Thouless transition, including a universal jump in the nonlinear resistance exponent. Compared tof=0, the transition is shifted to much lower temperatures. Nearf=1/2, below the transition temperature, single vortex crossings dominate the resistance. The transition atf=1 is qualitively the same as thef=0 Kosterlitz-Thouless transition, but small deviations are found. Forf=0.38, there is no experimental evidence for a special phase transition; over the whole temperature range, the resistance decreases exponentially with an energy barrier close to two in units of the Josephson coupling energy.     

Novel fabrication methods for submicrometer Josephson junction qubits

Novel processes for the fabrication of mesoscopic Josephson junction qubits have been developed, based on superconducting Al/Al₂O₃/Al tunnel junctions. These are fabricated by electron beam lithography using single-layer and multi-layer resists, and standard processes that are compatible with conventional CMOS processing. The new single-layer resist process is found to have significant advantages over conventional fabrication methods using suspended tri-layer shadow masks.     

Upscaling DC resistance using a Josephson junction array

A ratio standard for DC resistance measurements in the range above about 10 kΩ using a three-terminal Josephson junction series array is described. Resistance ratios of two-terminal resistors from 1:1 to at least 1:10 are examined with a single device utilizing the voltage steps of the Josephson array as voltage sources of a potentiometer bridge configuration. Some features of the circuit are discussed. The system promises systematic ratio errors below 10^-8 and uncertainties which depend only on the quality of the resistors. Preliminary measurements with a prototype instrument show a relative reproducibility of 1×10^-7, limited by the noise of a commercial digital multimeter used as a detector     

A novel ternary logic circuit using Josephson junction

A novel Josephson complementary ternary logic (JCTL) circuit is described. This fundamental circuit is based on the combination of two SQUIDs (superconducting quantum interference devices), one of which is switched in the positive direction and the other in the negative direction. The JCTL can perform the fundamental operations of AND, OR, NOT, and Double NOT in ternary form. The principle of the operation and design criteria are described in detail. Simulation results show that reliable operation of these circuits can be achieved with a high performance     

Direct-coupled high speed adder by using Josephson junction

This paper presents the latest design work of high speed adder logic based on Josephson elements. The Josephson adder uses a novel exclusive-OR logic and performs high speed carry propagation technique. The idea of directionality is also undertaken to avoid the necessary distortion in carry signal. The principle of operation with salient feature of simulation of the adder are presented in full detail. Necessary checks for carry skip and other fabrication parameters are investigated using detailed model of the device based on its highly miniaturized size. The results of the simulation show that the nominal delay of the adder logic is 20 ps/stage and average power dissipation is 47 μW/stage. Authors have mainly stressed upon how to obtain ultra fast speed at the cost of very low power dissipation of the presented adder with its small size.     

A new type of biepitaxialc-axis tilted YBCO Josephson junction

A novel fabrication procedure of high critical temperature superconductor Josephson junctions (HTCSJJ) has been developed by a 90° rotation of YBa₂Cu₃O_7?x c-axis around an in-plane direction, on the basis of concepts of the biepitaxial technique. YBa₂Cu₃O_7?x grows oriented along (001) direction on a MgO seed layer deposited on a (110) SrTiO₃ substrate and along (110) direction on the bare substrate. Josephson junctions of good quality were obtained exhibiting RSJ behavior and features characteristic of HTCSJJ phenomenology. Even if not uniform, in some samples, the nature of the critical currentI _c is completely Josephson, as resulting from theI _c dependence on the applied magnetic field. The maximum measuredI _c R _N value atT=4.2K is 2mV.