McCumber Parameter Research Articles

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.

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.

Synchronization of strongly interacting overdamped Josephson junctions

AbstractThe high frequency approximation is applied for the description of phase locking in the chain of two junctions loaded by the arbitrary resonance system providing strong coupling. The derived equation of synchronization describes phase locking for junctions which McCumber parameters of an order of magnitude larger than those described in ranges of the slowly varying amplitude approximation. The developed method is applied to the chain of junctions loaded by a resonant transmission line. Obtained values of the voltage locking interval and the maximal tolerant spread of critical currents are in agreement with numerical calculations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

NONEQUILIBRIUM CHARACTERISTICS OF INTRINSIC Bi2.3Pb0.1Sr2CaCu2O8+y JOSEPHSON JUNCTIONS

Using photolithography and Ar ion milling, we fabricate small mesas on top of the Bi 2.3 Pb 0.1 Sr 2 CaCu 2 O 8+y single crystals to study the inherent tunnelling property of intrinsic Josephson junctions. The I-V characteristics of the mesas show a typical multiple branches with large hysteresis. The return current I r depends on the N-th branch. The relation of I r and N follows I r= I 0* N m, where -1< m <0 might be related to the Coulomb blockade effect. The McCumber parameter βc of the samples is also investigated.

CHARACTERISTICS OF SINGLE INTRINSIC JOSEPHSON JUNCTION

A single intrinsic Josephson junction has been observed in a Bi 2.3 Pb 0.1 Sr 2 CaCu 2 O 8 mesa structure. The isothermal voltage-current curves with hysteresis were measured from 5K to 65.09K. The critical current of the junction is almost a constant while the return current depends on the temperature. The temperature dependence of jumping voltage spacing deviates strongly from the BCS one. The temperature dependence of McCumber parameter βc is shown.

Is it possible to fabricate a relaxation oscillation SQUID, using high temperature superconductors and grain boundary junctions?

We discuss whether it would be possible to fabricate Relaxation Oscillation SQUIDs (ROSs) using high temperature superconductors (HTSs). This would require HTS junctions with significant hysteresis at high temperatures and we have attempted to induce this using external capacitive shunts. We achieved McCumber parameter values as large as /spl beta//sub c/=4.5 at 40 K and were able to maintain /spl beta//sub c/>1 to 72 K. However we found that small junction resistances, thermal noise associated with high temperature operation and transmission line resonances in the shunt capacitor limit the value of /spl beta//sub c/. Using the parameters we obtained, we have simulated the performance of a ROS at 60 K and found that voltage pulses were generated. However, the small time averaged voltage across the ROS, would make it impossible to construct a working D-ROS. Despite this, it may be possible to detect the pulses and use them to construct a digital SQUID.

Synchronization of overdamped Josephson junctions shunted by a superconducting resonator

Synchronization was investigated numerically as well as by the method of slowly varying amplitudes for two Josephson junctions with McCumber parameters near 1 shunted by a superconductor and a dividing capacitor building up a resonator for ac currents. Because of the current resonance in the system the synchronizing ac current increases and provides phase locking up to 15% spread of critical currents. Thresholds of the phase-locked state at small as well as at large values of system parameters were explained in the developed model. Conditions of forming the phase-locked state are investigated in the many-junction array in which ac currents between neighbor junctions are formed through the superconducting shunt with a divided capacitance. It is shown that at certain conditions the total phase locking of all junctions switched into the voltage state appears when their quantity exceeds some critical value.

Discrete breathers in Josephson ladders

We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups [Phys. Rev. Lett. 84 (2000) 741; Phys. Rev. Lett. 84 (2000) 745; Phys. Rev. E 62 (2000) 2858]. We review the experiments made by Trı́as et al. [Phys. Rev. Lett. 84 (2000) 741]. We report the detection of different single-site and multi-site breather states and study the dynamics when changing the array bias current. By changing the temperature we can control the value of the damping (the Stewart–McCumber parameter) in the array, thus allowing an experimental study at different array parameters. We propose a simple DC circuit model to understand most of the features of the detected states. We have also compared this model and the experiments with simulations of the dynamics of the array. We show that the study of the resonances in the ladder and the use of harmonic balance techniques allow for understanding of most of the numerical results. We have computed existence diagrams of breather solutions in our arrays, found resonant localized solutions and described the localized states in terms of vortex and antivortex motion.

LC-resonant voltage response of superconducting quantum interference filters

The voltage vs. magnetic field relation V(B) of superconducting interferometers consisting of two or more Josephson junctions is the basic characteristic of their operation as highly sensitive magnetometers and amplifiers. The conversion efficiency /spl part/V//spl part/B of interferometers containing two Josephson junctions, i.e. dc SQUIDs, decreases significantly with increasing loop inductance L. Therefore, the range of SQUID loop sizes for which the SQUID operates properly is very restricted. However, for sufficient coupling between the SQUID and the signal coil a large value of L is desirable. In this work theoretical and experimental results on the voltage response function of quantum interference filters (SQIFs) are presented. A SQIF consists of N Josephson junctions connected in parallel to form a 1D array. The array loop sizes are chosen such that the voltage response becomes a unique function around B=0. It is shown that for McCumber parameters /spl beta//sub C/>0.5 and sufficiently large array inductances the V(B) relation of SQIFs shows LC-resonances that lead to two pronounced minima in the response function. In the LC-resonant operation mode the conversion efficiency of SQIFs is not degraded even for large array inductances. By this, a very strong coupling to signal coils can be achieved. The experimental results agree very well with the theoretical predictions on which basis the SQIF has been fabricated.

YBa 2 Cu 3 O 7 Josephson junctions on LaAlO3 bicrystals for terahertz-frequency applications

We prepared Josephson junctions made of YBa2Cu3O7 on symmetric 24° LaAlO3 bicrystal substrates. For better coupling of high-frequency radiation, we structured the contacts with logarithmic-periodic antennas made of YBa2Cu3O7. Characterization was done by measuring the voltage–current characteristics to determine the critical current IC, the normal-state resistance RN, the noise parameter Γ, and the Stewart–McCumber parameter βC as predicted by the resistively and capactively shunted junction model (RCSJ). The junctions showed excellent RCSJ-like behavior with ICRN products of up to 2.0 mV at 10 K and 220 μV at 77 K. To demonstrate the possibility to detect high-frequency radiation up to the THz regime, we used the Josephson junction as a detector for radiation from a far-infrared laser and we reconstructed the spectra by Hilbert spectroscopy.

Stable ground states for Δϕ=π in double Josephson junction superconducting loops

We examine the origin of Josephson junctions with phase difference π through the dynamics of coupled Josephson junctions. We show that in a superconducting loop with an asymmetrical double junction, ground states with Δϕ=π can naturally occur. We show further that the ground state of the coupled system can possess energy minima that are deeper at nπ for n odd than n even depending upon the ratio of the critical currents in the two junctions and the McCumber parameter of the individual junctions.

Bit error rate experiments in ring-shaped RSFQ circuits

Ring-shaped rapid single flux quantum (RSFQ) circuits composed of segments of Josephson transmission lines (JTLs) and other RSFQ circuits enable permanent SFQ pulse circulation. New ring structures of different designs have been realized which comprise T-flipflop (TFF) and multiplier (MULT) circuits. Reliability in circuit operation has been proven experimentally by a bit error rate BER ≅10 −16 . The fabrication process has been optimized by using PTB-4 μ m Nb/Al 2 O 3 –Al/Nb trilayer technology with externally shunted tunnel junctions of critical current densities of j c =≅1 kA/cm 2 . Characteristic voltage is V c =250 μ V and Steward–McCumber parameter β c ≤1. A linear dependence of pulse circulation frequency on JTL bias currents has been measured within a bias current interval of 20%.

Effects of capacitive shunt on the current-voltage characteristics of high T/sub c/ Josephson junctions

We have studied hysteresis of the grain boundary YBa/sub 2/Cu/sub 3/O/sub 7/ Josephson junctions with Au film shunt capacitors. The capacitive shunt clearly developed hysteresis in the current-voltage curves of the junctions. However, the McCumber parameter /spl beta//sub c/, obtained from data was much smaller than the calculated values. The reason is believed to be due to the fact that the capacitive reactance was dominated by the kinetic inductance of the bridge and the series resistance of the Au film connecting the two capacitors structured on both sides of the electrodes. Using a superconducting capacitor built directly on the bridge will enhance the hysteresis. More study is needed on the inductive shunt in the junction.

Josephson junctions with hysteretic current voltage characteristics at high temperatures

The properties of bicrystal Josephson junctions with external capacitors are reported. It was found that the hysteresis in the current voltage (IV) characteristic was very sensitive to the wavelength of the Josephson oscillation in the dielectric and thermal noise suppression of the critical current. A McCumber parameter /spl beta//sub c/ of 1.2 at 65 K has been achieved. In addition intrinsic grain boundary capacitance has been found to give a large /spl beta//sub c/ value of 9.6 at 4.2 K.

Broadband SQUID amplifiers for photonic applications

The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.

Oscillation spectral linewidth for some phase-locked Josephson-junction arrays

High effective autoregressive method has been applied to the calculation of the oscillation line width for the promising phase-locked Josephson-junction arrays. It has been found, that the oscillation linewidth decreases with the number N of Josephson junctions proportionally to N for one-dimensional arrays or even more fast for two-dimensional arrays until number N exceeds the coupling radius. It has been shown that in the case of parallel array inserted into superconducting microstrip line, the phase-locked oscillation state in-phase could be provided by the strong interaction between Josephson junctions and electromagnetic standing wave regardless to applied magnetic field. The necessary amplitude of the standing wave is easy attained at McCumber parameter value /spl beta/>1, when the high-frequency Josephson-junction impedance is small in comparison with the strip-line wave impedance. An extra reduction in the linewidth caused by electromagnetic standing wave impact has also been studied. The results are discussed from viewpoint of the possible applications of the structures as submillimeter wave generators.

Effect of an input coil microwave resonance on dynamics and noise properties of a dc superconducting quantum interference device operating close to the hysteretic mode

The dynamics and noise of a dc superconducting quantum interference device (SQUID) with the McCumber parameter βc=2πR2IcC/Φ0 close to the unity (where Ic, R, C are the critical current, the shunt resistance, and the capacitance of the Josephson junctions comprising the SQUID, respectively, and Φ0=2.07×10−15 Wb is the magnetic flux quantum) integrated with a planar spiral input coil have been experimentally studied. The length of the spiral input coil was chosen to match its λ/4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance enhances the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, increases the dynamic resistance Rd and the gradient of the flux-to-voltage characteristics ∂V/∂Φ without hysteresis. This relaxes the tolerance for the βc parameter, simplifies the technological process, and improves the yield of devices. A dc SQUID with loop inductance L=31.4 pH, βc=0.72, and a six turn input coil has demonstrated a nondistorted quasisinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of approximately 140 μV peak-to-peak. A spectral density of the intrinsic magnetic flux noise as low as 3.5×10−7 Φ0/Hz1/2 has been measured in the double stage configuration at a temperature of 4.2 K using direct read-out electronics. This corresponds to the intrinsic energy resolution of ε=12.5h. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz1/2 with an input coil inductance of 58 nH. The coupled energy resolution is εc=45h in the white noise region.

Dynamics and chaos of a current driven two-dimensional Josephson junctions array under [formula omitted] magnetic field

We derive the equations of motion for a two-dimensional capacitive Josephson junctions array in the presence of both a DC current and a magnetic field f= 1 3 of the quantum flux Φ 0 . The ground state symmetry of an N× N array is assumed to hold for all currents, then by using the resistively and capacitively shunted junction equations, a model system of four-coupled non-linear second-order differential equations is derived. The system has the form β c x ″+ x ′+∇ U=0, where U is a four-dimensional potential and β c is the Stewart–McCumber parameter. The dynamics can be viewed as the motion of a massive particle sliding under the action of the potential in a four-dimensional configuration space with a friction proportional to its speed. There are three distinct branches: one below the critical current I c where the static zero voltage solution is stable; the second branch which originates from the static solution through a Hopf bifurcation and where a total voltage develops along the direction of the applied current and across the array (instantaneous Hall voltage), (the latter means vortices moving perpendicular to the current and constitutes a flux-flow like regime); and a third branch above the synchronization current I s , where the motion of the junctions synchronizes and the motion of the vortices ceases with zero Hall voltage. For a wide range of β c , the second branch shows chaotic dynamics of extremely rich complexity. A pervasive feature is the presence of antimonotonicity, i.e., reversals of period doubling cascades.

Processing of Nb DC SQUIDs for RF amplification

DC SQUIDs amplifiers based on Nb/Al–Al 2O 3/Nb Josephson junctions technology have been designed, fabricated and characterized. To compare the RF performances as a function of the device layout, several types of SQUIDs with various washer inductances and different input transformers have been fabricated on the same wafer. A seven mask process has been set up to fabricate the SQUID amplifiers without anodization steps. The geometric and electronic parameters of the different device elements and the spread of the fabrication parameters have been studied. Critical steps such as the reliable fabrication of 4 and 9 μm 2 area Josephson junctions, the control of their critical current density between 300 and 1000 A/cm 2, the SiO 2 interlayers quality, and the step coverage have been characterized and optimized. Maximum voltage modulation Δ V and flux to voltage transfer function δV/ δΦ as high as 450 μV and 1500 μV/Φ 0, respectively, have been found. Δ V and δV/ δΦ variation with the screening parameter β L =2 LI 0/Φ 0 and with the McCumber parameter β C have been investigated and the dependence of a typical device gain with frequency in the 1–200 MHz range is presented.