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Physical review. B, Condensed matter

I-Vcharacteristics of microwave-driven Josephson junctions in the low-frequency and high-damping regime

C. Vanneste, C. C., Karen H. Brown, Agnese Callegari, M. M. Chen, J. H. Greiner, Harold Cedric. Jones, K. K. Kim, Alan W. Kleinsasser, Harris Notarys, George R. Proto, R. H. Wang, T. Yogi

Published Apr 1, 1985• 22 citations
Publisher

Abstract

Experimental I-V curves of microwave-driven Josephson tunnel junctions with resistive shunts are reported. The results are in very good agreement with numerical calculations using the resistively shunted junction model. In the low-frequency regime there are three distinct regions in the I-V curves and two different types of Shapiro steps. It is demonstrated that the overall shape of the I-V curves can be explained by using an adiabatic interpretation of the junction response. The two different types of Shapiro steps are related to a compensation effect between dc and rf bias currents.

DOI
10.1103/physrevb.31.4230

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Experimental I-V curves of microwave-driven Josephson tunnel junctions with resistive shunts are reported. The results are in very good agreement with numerical calculations using the resistively shunted junction model. In the low-frequency regime there are three distinct regions in the I-V curves and two different types of Shapiro steps. It is demonstrated that the overall shape of the I-V curves can be explained by using an adiabatic interpretation of the junction response. The two different types of Shapiro steps are related to a compensation effect between dc and rf bias currents.
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.
We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.
We have investigated theoretically the amplitudes of RF- induced constant voltage steps in two-dimensional Josephson tunnel junctions, using both a first-order approximation and a numerical it- eration procedure to calculate the current density distribution in the junction. We use a planar resonator model to analyze the electromag- netic field in the microwave-driven junction. Integrating the local Jo- sephson current density over the junction area yields the total dc current on a chosen Shapiro step. Numerical calculations of the Sha- piro step amplitudes in two-dimensional resonant junctions show a qualitatively different behavior from that in one-dimensional resonant junctions. Depending on the dominant resonant mode, the microwave power dependence of the step amplitude gives a smooth curve without zeros. This behavior is advantageous for biasing the Josephson junc- tion in its maximum step amplitude. The main difference between the results of the first-order approximation and the full theory is that- using the iteration procedure-the Shapiro steps in resonant junctions become asymmetric with respect to the quasi-particle curve. This is due to consideration of the losses and the internal Josephson currents in the numerical iteration procedure of the full theory.
An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed.
The dc characteristics of superconducting point-contact junctions subjected to external noise currents are measured under the condition that the noise-frequency spectrum is below the Josephson frequency. It is shown that the curves are in agreement with a model based on modulation of the noise-free dc characteristic. Although in the low-bias-voltage region the shape of the curves is qualitatively similar to previous theoretical predictions for the case of high-frequency noise, for higher voltages the shapes are different. Quantitative differences exist over the whole range of bias voltage.