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Journal of Applied Physics

Radio-frequency properties of stacked long Josephson junctions with nonuniform bias current distribution

Giovanni Filatrella, N. F. Pedersen

Published May 1, 1999• 1 citation
Publisher

Abstract

We have numerically investigated the behavior of stacks of long Josephson junctions considering a nonuniform bias profile. In the presence of a microwave field the nonuniform bias, which favors the formation of fluxons, can give rise to a change of the sequence of radio-frequency induced steps. The amplitude of the steps is enhanced when the external frequency matches the fluxon shuttling regime.

DOI
10.1063/1.370210

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IEEE Transactions on Magnetics•May 1, 1983•1 citation
We have numerically investigated the behavior of stacks of long Josephson junctions considering a nonuniform bias profile. In the presence of a microwave field the nonuniform bias, which favors the formation of fluxons, can give rise to a change of the sequence of radio-frequency induced steps. The amplitude of the steps is enhanced when the external frequency matches the fluxon shuttling regime.
During last decade, considerable efforts were made to achieve coherent emission from stacks of many Josephson junctions. It is known that strong emission from a junction in the presence of external magnetic field appears at the so-called Fiske steps in the IV-characteristic at voltages which correspond to frequencies of geometrical resonances. However, it is possible to obtain resonant steps in long junctions without external magnetic field. The periodical movement of fluxons is excited due to some disorder in the distribution of critical currents along junctions. The so-called zero-field steps are formed in the IV-curve due to the interaction of fluxons with oscillations of voltage at Josephson frequencies. We investigated numerically IV-characteristics and the dependence of the average square of ac voltage at the end of the stack of two long Josephson junctions on the average voltage. Junctions interacted inductively with each other. We introduced not only the Gaussian distribution of critical currents along junctions but also the Gaussian distribution of coefficients of the interaction between junctions (mutual inductances). Zero-field steps in the IV-characteristic were found at voltages which corresponded to frequencies of in-phase collective modes in the stack as well as to frequencies of uncoupled junctions. Zero-field steps appeared in the hysteretic region of the IV-curve. There appeared also jumps of voltage from the resistive branch to the zero-field step. We showed that there existed distributions of mutual inductances along junctions which provided jumps to voltages at which the average square of ac voltage at the end of the stack (which is proportional to power of emission) was larger than that for the stack with the uniform distribution of mutual inductances.
We have recorded the radiation generated by magnetic flux quanta oscillations and by cavity mode oscillations in two-stacked arrays each consisting of five long Josephson junctions biased in parallel. The two arrays have in common the middle electrode, which is thinner than the London penetration depth, and can be biased independently. Basically, two kind of fluxon states can be generated, one consisting of a row of five fluxons oscillating in one of the arrays, the other consisting of a row of five fluxons in one array and five antifluxons in the other array, bound in a coherent state. It is found from the microwave emission that the latter configuration is less sensitive to low-frequency noise.
The amplitudes of the current steps in the I-V characteristics of mutually coupled two-dimensional distributed Josephson tunnel junctions driven by microwaves are investigated. For this purpose a numerical computation algorithm that is based on a planar resonator model for the individual Josephson tunnel junctions is used to calculate the DC current density distribution. In addition to the fundamental microwave frequency, harmonic contents of the tunneling current are also considered. The lateral dimensions of the individual junctions are small compared to the microwave wavelength and the Josephson penetration depth, giving an almost constant current density distribution. Therefore, the coupled junctions can give much greater step amplitudes than a single junction with an equal tunneling area, because of their nonuniform current density distribution. The calculation show a strong dependence of the Shapiro step amplitudes with respect to the coupling of the tunnel junctions. These studies imply that the choice of proper coupling conditions is important to achieve maximum step amplitudes. These results are helpful in designing tunnel junctions with optimized step amplitudes.
Large constant voltage-current steps were observed in the I-V characteristics of long NbN-MgO-NbN Josephson junctions in the presence of external magnetic fields of a few Gauss. The steps are separated by a voltage corresponding roughly to three to five times the voltage spacing expected between adjacent Fiske steps. Models addressing the origin of such steps are presented. Simultaneous nucleation of fluxons at several sites along the junction with thin electrodes, favored by the large London penetration depth of NbN, would introduce a large amount of magnetic flux into the junction at once, leading to large steps. A model which involves pinning of fluxons in the junction is given. Due to the granularity of NbN and its very small coherence length, there will be pinning sites in the junction preventing single fluxons from moving at low bias currents. At particular junction parameter values the steps become very regular and sharp. The sharp steps can be used as a voltage standard without external RF bias or as a high-power oscillator when the device is suitably biased.>
Extensive measurements of radiation emitted from long Josephson junctions d.c.-current biased on zero-field and Fiske-steps are reported. The measurements were made in the band 8-10 GHz on long Nb-Nb oxide-Pb overlap tunnel junctions with the lengths 0.5 mm and 1.0 mm having fundamental frequencies of 10 GHz and 5 GHz, respectively. Depending on the fundamental frequency of the junction 1st or 2nd harmonic detection was employed. In the fundamental scheme the frequency f n vs. the d.c.-voltage V n along the steps follows a modified Josephson voltage/frequency relation f n / V n = 2 e/nh , where n is the step-number n = 1, 2, 3,... for Fiske-steps and n = 2, 4, 6,... for zero-field steps. On a given step the frequency could be tuned (200-500 MHz) by varying the bias point. The linewidth was measured to be less than 5 kHz. All the observed phenomena are consistent with a novel unified dynamic bunched fluxon model applicable to both zero-field and Fiske-steps and are in good agreement with recent numerical solutions of the perturbed sine-Gordon equation with proper boundary conditions. Taking advantage of operation on higher order steps and strong harmonic generation the present upper frequency limit for the Josephson fluxon oscillator is above 200 GHz. The maximum power observed so far is only 5 pW, but the estimated available power is of the order 1 μW, which is quite sufficient to pump other Josephson devices.