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IEEE Transactions on Applied Superconductivity

Modeling of the josephson fluxonic diode

Farshid Raissi

Published Sep 1, 2003• 9 citations
Publisher

Abstract

A forward bias Josephson fluxonic diode exhibits a linear I-V curve whose slope is a function of the Stewart-McCumber loss parameter /spl beta/, the length of the junction, critical current density and the magnitude of the applied control current. This linear I-V curve lacks resonance structure and does not exhibit a flux flow step. A modeling which matches experimental results is presented.

DOI
10.1109/tasc.2003.817638

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A forward bias Josephson fluxonic diode exhibits a linear I-V curve whose slope is a function of the Stewart-McCumber loss parameter /spl beta/, the length of the junction, critical current density and the magnitude of the applied control current. This linear I-V curve lacks resonance structure and does not exhibit a flux flow step. A modeling which matches experimental results is presented.
With a slight modification to the control line and its bias configuration, a long Josephson junction vortex flow transistor structure can become a so-called fluxonic diode containing fluxon and antifluxon "doped" regions in analogy to a pn junction. Such structures have been made with Nb-Pb tunnel junctions allowing testing of the same device with a number of different doping configurations. This paper compares experimental results with a one dimensional numerical simulation. Different configurations for the diode have been modeled with Stewart-McCumber loss parameters ranging between 50 and 1400. The simulation clarifies the origin of a number of experimental observations, including a peculiar dependence of resonance induced step behavior on loss parameter, and a limit to the value of the gradient of doping in the transition region below which an asymmetric I-V curve representing forward and reverse biases is obtained. In forward bias, the I-V curve above a threshold current is roughly linear and devoid of resonance structure, provided injection of carriers occurs from one region to the other. Injection is a function of loss and the asymmetry of doping.>
Josephson Fluxonic Diode (JFD) provides a very nonlinear characteristic in comparison with a long Josephson junction at microwave frequencies. This nonlinearity is highly accentuated by creation and dynamics of vortex-antivortex pairs in two disparate modes of operation; forward and reverse-bias. Experimental detection of microwave frequencies through this device is not solely dependent on the geometry and seems to change drastically with the different operating condition. This paper attempts to understand the microwave characteristic of this device with respect to its bias and control current and rf-exposed boundary conditions defined in RCSJ model of JFD. Based on the simulation results, for a finite length of a JFD excited by a low-amplitude microwave signal below its plasma frequency, control current increases the rate of vortex-antivortex pair generation and fine-tunes the microwave resistance (Rω) up to an order of magnitude more than its zero magnetic field resistance (R0). Under this circumstance, adding the bias current which can move generated vortex-antivortex pairs causes a substantial increase up to three orders of magnitude compared to R0either in forward or reverse-bias, while damping coefficient 1/√βc(βcis Stewart-McCumber parameter of Josephson junction) can limit this increase. It has also been shown that the variation of polarity, frequency, or amplitude of incoming microwave signal can impact on the impedance due to its relation with pair generation rate and so causes variations in observed impedance both in linear and nonlinear form. According to the results, low-microwave impedance of a JFD can be multiplied externally using biasing sets to match with high-impedance sources, which justifies its detection mechanism at microwave frequency.
Josephson fluxonic bipolar junction transistor (JFBJT) has been proposed as a superconducting amplifying element. The results on a simple realization of this device are provided to demonstrate its working principle. These experiments demonstrate that JFBJT provides current gain without suffering from the problems associated with the regular long junction vortex flow transistors. In particular, no resonance structure is present in its I-V characteristics and its impedance can be matched to any load without degradation of its characteristics. Suggestion is made on how a practical device can be fabricated.
We have investigated numerically a system consisting of a long Josephson junction embedded into a microstrip resonator. For such a configuration the Josephson vortex dynamics in the junction is driven by the oscillating currents in the resonator. We have calculated the complex impedance of the junction at the resonant frequency. The Q factor of the resonator and the change of the resonant frequency of the whole system can then be easily calculated knowing the parameters of the resonator without Josephson junction. The fluxon dynamics and the complex impedance of the junction are simulated for different values of the junction length, damping, dc bias current, and dc magnetic field. This allows us to explain the behavior of the impedance of the junction and different loss mechanisms. In particular, we predict a nonmonotonic dependence of the both real and imaginary parts of the impedance on the amplitude of the oscillating current in the resonator for some range of parameters. Our results show that such a combination of active and passive superconducting elements forms a rather interesting nonlinear physical system which might be useful for development of tunable/switchable superconducting resonators and suggests an experimental technique for detecting trapped vortices in long junctions.
The first object of this work is to theoretically study the effects of tunnel junction parameters on flux-flow Josephson oscillators (FFOs) by numerical simulation and to experimentally study the rf properties of FFOs by integrating them together with an SIS (superconductor-insulator-superconductor) mixer/detector on a chip. By using a CAD modeled integrated sub-mm wave receiver, the composite linewidth of two FFOs was measured to be less than 2.1 MHz in the band 280-330 GHz. The receiver consists of two identical FFOs and an SIS mixer. The linewidth was determined by mixing the two signals in the SIS mixer and analyzing the intermediate frequency. The output power coupled to a 10 .OMEGA. microstripline was about 0.5 µW, and could be adjusted by changing the current bias of the oscillator. The FFOs are connected to the SIS mixer via interdigital capacitors. The FFOs and the SIS element are made of Nb/NbOx/PbBi junctions by the "reactive ion beam oxidation" technique with the critical current density jc controlled by the oxidation time. Lift-off stencils for defining the junction sizes and the top-electrodes were made by using electron-beam writing on PMMA/Copolymer double layer resist. The jc of a long Josephson junction (LJJ) determines the fluxon motion. For LJJs which had jc > 1 kA/cm2, velocity-matching (VM, where the phase velocity of propagating fluxons equals that of the electromagnetic wave in the LJJ) steps could be tuned linearly from about 0.2 to 1.4 mV by an applied magnetic field. Coupled radiation at around 100 GHz (about 3 nW), 261 GHz (4.6 nW), and 330 GHz (0.43 µW), from flux-flow oscillations, was observed. From the step's steepness, the junction quality factor QJ is determined. QJ is between 4 to 7 in the voltage range of 0.4 to 1 mV. Coupled radiation (> 3 nW) at around 100 GHz corresponding to resonant soliton oscillation in low jc samples (250 to 1000 A/cm2) was detected. Simulations show that, for a uniform bias feed, the height of the VM step .gammam increases almost linearly with the external magnetic field .beta.e and the quasiparticle loss .alpha., but is less dependent on the surface loss .beta.. An approximate expression .gammam = a + .alpha(1+b).beta.e agrees with simulations. The maximum ac output voltage decreases with increasing dampings .alpha. and .beta.. It is important to include the .beta.-term in the mathematical model. The second part of this work is devoted to rf properties of long YBa2Cu3O7-.delta. (YBCO) grain boundary junctions made on 0- 32 °. [001]-tilt YSZ bicrystals. Josephson flux-flow resonances and Fiske resonances were observed. The first resonances could be tuned from about 0.5 to 2.0 mV in a 30 µm long junction at 16 K, and we determined the ratio between barrier thickness and relative dielectric constant td/.epsilon.r=2.9 Å and the loss .alpha.= 1.3 at 16 K. Simulations support the experimental observation that Josephson vortices can propagate unidirectionally in an overdamped, homogeneous junction up to .alpha.Ã? 2. From the Fiske resonances at 256-638 GHz, their Q-values, and the Steward-McCumber parameter, we find td/.epsilon.r=4 Å, the London penetration depth .gamma.L=145±5 nm and the surface resistance RS ~20 m.OMEGA. at 280 GHz. We conclude that the boundary is dielectric and the YBCO grains are well superconducting within 5-20 nm from the boundary. The dielectric between the grains could be part of a tunnel barrier and/or a matrix for filamentary conduction. Josephson flux-flow transitors based on long bicrystal junctions were made with an Au loop used as the control line. The line modulated the critical current Ic. Current gain larger than unity was obtained below 70 K. The gain increased with the junction length and varied roughly like the square root Ic when adjusting the temperature. A transresistance larger than 5 .OMEGA. was obtained at 15 K. Better performance is expected from junctions with high current densities.
Theoretical and experimental studies have been made of the effects of junction geometry on the performance of the flux-flow type Josephson oscillator. It is shown theoretically that the height and the slope of the current steps appearing in dc I-V curves of the junction, which determine the available power and the radiation linewidth of the oscillator, respectively, are dependent strongly upon self fields in the junction. In order to study the effects of junction geometries on the self fields, computer simulation and experiments have been carries out for an in-line junction, an overlap junction and an overlap junction with a small projection on one side. The best performance is obtained for the overlap junction with a moderate projection on side as expected theoretically.