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Acta Physica Sinica

THE STEP STRUCTURES EFFECT OF DC JOSEPHSON CURRENT WITHIN ONE FLUX QUANTUM PERIOD φ0(Ⅱ)—— JOSEPHSON JUNCTION WITH LARGER DIMENSIONS

ZHANG YU-HENG, SHEN XIU-LING, ZHENG JIE-FEI, 吴彦, WANG MAO-QUAN, (1)中国科学技术大学物理系; (2)中国科学技术大学物理系,82级研究生; (3)中国科学技术大学物理系,82届毕业生,现在美国UCBerkeley做研究生; (4)中国科学技术大学物理系,82届毕业生,现在中国科学院半导体研究所; (5)中国科学院等离子体物理研究所

Published Jan 1, 1984• 0 citations
Publisher

Abstract

We point out that by placing a large Josephson junction in high Q-value cavity whose rth eigen mode is excited by the Josephson frequency ω0=2cV0/h, the oscillating electromagnetic field will act on the juntion and one must recognize that the space part of the eigen mode of the field are not the same on the junction. We have obained theoretical result which is different from paper [2] and shows how the step structure current vary with the magnetic field. The match condition for eigen mode of the feedback field from the cavity and electromagnetic field radiated by Josephson junction has been worked out. Finally, the physical reason for the absence of step structure with period less than φ0 is given.

DOI
10.7498/aps.33.1075

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Cavity-mode excitation in a Josephson tunnel junction

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Using Takanaka's theory of the zero-field dc-current steps of a Josephson tunnel junction, we have studied the effect of the junction $Q$ factor on the shape of the current step near the first even-order resonant voltage $V=h\frac{{\ensuremath{\nu}}_{c}}{e}$, where ${\ensuremath{\nu}}_{c}$ is the frequency of the fundamental cavity mode. In addition, we have found that the effect of a magnetic field on the step height can be qualitatively explained by modifying Takanaka's theory to include a magnetic-field-dependent term.

Physical review. B, Condensed matter•Sep 1, 1980•15 citations
We point out that by placing a large Josephson junction in high Q-value cavity whose rth eigen mode is excited by the Josephson frequency ω0=2cV0/h, the oscillating electromagnetic field will act on the juntion and one must recognize that the space part of the eigen mode of the field are not the same on the junction. We have obained theoretical result which is different from paper [2] and shows how the step structure current vary with the magnetic field. The match condition for eigen mode of the feedback field from the cavity and electromagnetic field radiated by Josephson junction has been worked out. Finally, the physical reason for the absence of step structure with period less than φ0 is given.
In this paper, we analyzed the physical essence for producing a series of step structures or oscillating effect of dc Josephson current within one flux quantum period φ0 by placing Josephson junction, two-junction SQUID and the supercon ducting ring containing a single junction in a cavity, when one of the eigen-frequencies ωr of which is equal to Josephson frequency and the Q-Value is sufficiently high. We point out that the frequency effect of the feedback field would produce a series of induced steps for Josephson junction or two-junction SQUID, as ω = ωr, the oscillating electric-magnetic field excited by the junction current reacts on the junctions themself. Furthermore, a series of new step structures should occur within the φ0 since the amplitude of the feedback field is modulated by applied magnetic field as the modulation of the amplitude of the feedback field is coupled with that of the radiation. For the superconducting ring containing a single junction, as nω=ωr, the feedback radiation of stationary electric-magnetic wave will give rise constrained oscillation of the supereurrent with a smaller period than the φ0.
This paper investigates the physical nature of a series of step structures or oscillations present in a Josephson current within one magnetic flux quantum when either a Josephson junction, a double junction squId, or a single junction superconducting ring is placed inside a high Q cavity under the condition in which the Josephson frequency is equal to the resonance frequency of the cavity. The frequency effect of the feedback field produces a series of induced current steps in the Josephson junction or the two-junction squId when ..omega.. = ..omega../sub r/. The oscillating electromagnetic field excited by the junction current acts on the junction itself. A series of new current step structures occur within one magnetic flux phi/sub 0/ quantum, since the amplitude of the feedback field is modulated by an applied magnetic field as the modulation of the amplitude of the feedback field is coupled to that of the radiation. For the superconducting ring containing a single junction, as n..omega.. = ..omega../sub r/, the feedback radiation of the stationary electromagnetic wave will give rise to a constrained oscillation of the supercurrent with a period smaller than that of the superconducting current oscillation phi/sub 0/.
If a SQUID consisting of two junctions is placed in a cavity with sufficiently high Q-value, when the Josephson frequency of the junction ω=2eV0/h equals to one of the ei-gen frequencies ωr of the cavity, then the oscillating electromagnetic field in the form of standing wave excited by the junction current would react on the junctions and produce a series of steps of dc Josephson current within one flux quantum period Φ0. The theory also predicts that a series of new superconducting quantum interference phe-nomenons would be produced by Josephson currents of two junctions in the feed back field. The step height of the Josephson current will be inreased when both junctions are placed separately at the peak of the standing wave. The phase of the interference trace of SQUID will change by π/2 when one of the junctions is placed at the peak and the other is placed at the trough. The I-H trace of SQUID will degenerate to that of signle junction when one of the junctions is placed at the pack and the other is placed at the node. The step will not occur except that with n=0 yhen both junctions are placed separately at nodes.
High Tc Josephson junctions have IcRn products as large as a few mV at liquid helium temperature, and hence, the frequency normalized by IcRn∕Φ0 becomes on the order of 10−3 for a gigahertz (GHz) microwave signal. (Here, Ic, Rn, and Φ0 are the critical current, the normal resistance, and a flux quantum, respectively.) It is well known that a microwave-current-driven Josephson junction does not exhibit clear Shapiro steps under such low frequency conditions. Instead of Shapiro steps, however, we often observe a current-step-like structure in the current–voltage curve of YBa2Cu3O7−δ grain boundary Josephson junctions coupled to a GHz signal. In this article, we present a model analysis for such current-step-like structures. Two types of device models are employed: a simple resistively and capacitively shunted junction model and a rf-field-driven two-junction superconducting quantum interference device model. Numerical results of the latter model agree with the experimental results, which indicates that the envelope of small Shapiro steps, including the effects of microwave-induced motion of flux quanta, appears as a current-step-like structure in a high Tc Josephson device coupled to a GHz microwave.
It is pointed out that if a superconducting ring containing a weak link is placed in a cavity, which is in resonant with the current flowing in the ring, i.e., when the frequency of the Josephson current or one of its n-th harmonies is equal to the cavity frequency, and if the cavity has sufficiently high Q-value, then the feedback of the stationary electric-magnetic wave will act on the ring itself and produce a small sinusoidal oscillation superposing on the primary sawtooth wave oscillating current. The period of the small oscillation will be φ0/n and its amplitude that of the sawtooth wave multiplied by 1/nπ.
Using Takanaka's theory of the zero-field dc-current steps of a Josephson tunnel junction, we have studied the effect of the junction QQQ factor on the shape of the current step near the first even-order resonant voltage $V=h\frac{{\ensuremath{\nu}}_{c}}{e}$, where ${\ensuremath{\nu}}_{c}$ is the frequency of the fundamental cavity mode. In addition, we have found that the effect of a magnetic field on the step height can be qualitatively explained by modifying Takanaka's theory to include a magnetic-field-dependent term.