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Journal of Applied Physics

Capacitance measurement of Josephson tunnel junctions with microwave-induced dc quasiparticle tunneling currents

K. Hamasaki, Keiji Yoshida, F. Irie, Keiji Enpuku

Published May 1, 1982• 3 citations
Publisher

Abstract

The microwave response of the dc quasiparticle tunneling current in Josephson tunnel junctions, where the Josephson current is suppressed by an external magnetic field, has been studied quantitatively in order to clarify its characteristics as a probe for the measurement of the junction capacitance. Extensive experiments for both small and long junctions are carried out for distinguishing between microwave behaviors of lumped and distributed constant junctions. It is shown that the observed voltage dependence of the dc quasiparticle tunneling current modified by an applied rf field is in good agreement with a theoretical result which takes into account the influence of the microwave circuit connected to the junction. The comparison between theory and experiment gives the magnitude of the internal rf field in the junction. Together with the applied rf field, this internal rf field leads to the junction rf impedance which is dominated by the junction capacitance in our experimental condition. In the case of lumped junctions, this experimental rf impedance is in reasonable agreement with the theoretical one with the junction capacitance estimated from the Fiske step of the distributed junction fabricated on the same substrate; the obtained ratio of the experimental impedance to the theoretical one is approximately 0.6–1.7. In the case of distributed junctions, however, experimental values of their characteristic impedances are approximately 0.2–0.3 of theoretical values calculated by assuming the one-dimensional junction model and taking account of the standing-wave effect in the junction.

DOI
10.1063/1.331107

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The microwave response of the dc quasiparticle tunneling current in Josephson tunnel junctions, where the Josephson current is suppressed by an external magnetic field, has been studied quantitatively in order to clarify its characteristics as a probe for the measurement of the junction capacitance. Extensive experiments for both small and long junctions are carried out for distinguishing between microwave behaviors of lumped and distributed constant junctions. It is shown that the observed voltage dependence of the dc quasiparticle tunneling current modified by an applied rf field is in good agreement with a theoretical result which takes into account the influence of the microwave circuit connected to the junction. The comparison between theory and experiment gives the magnitude of the internal rf field in the junction. Together with the applied rf field, this internal rf field leads to the junction rf impedance which is dominated by the junction capacitance in our experimental condition. In the case of lumped junctions, this experimental rf impedance is in reasonable agreement with the theoretical one with the junction capacitance estimated from the Fiske step of the distributed junction fabricated on the same substrate; the obtained ratio of the experimental impedance to the theoretical one is approximately 0.6–1.7. In the case of distributed junctions, however, experimental values of their characteristic impedances are approximately 0.2–0.3 of theoretical values calculated by assuming the one-dimensional junction model and taking account of the standing-wave effect in the junction.
Experimental and theoretical studies are made of the effect of a microwave on dc current-voltage characteristics of long Josephson junctions. In the case of zero external dc current, dc voltages were observed when the microwave was applied to the junctions. By comparing the observed magnetic-field and microwave-power dependences with theoretical results, it is concluded that these dc voltages resulted from vortex motion which was induced by the applied microwave. When the junctions were in a flux-flow state caused by the external current, a good agreement between theory and experiment concerning the microwave-power and magnetic-field dependences of Shapiro steps demonstrates that an almost ideal traveling-wave type coupling between the applied microwave and a moving vortex array took place in the long Josephson junctions.
In this paper, we show theoretically and experimentally that the reactive quasiparticle tunnel current of the superconductor tunnel junction could be directly measured at specific bias voltages for the higher harmonics of the quasiparticle tunnel current. We used the theory of quasiparticle tunneling to study the higher harmonics of the quasiparticle tunnel current in superconducting tunnel junction in the presence of rf irradiation. The impact of the reactive current on the harmonic behavior of the quasiparticle tunnel current was carefully studied by implementing a practical model with four parameters to model the dc I-V characteristics of the superconducting tunnel junction. The measured reactive current at the specific bias voltage is in good agreement with our theoretically calculated reactive current through the Kramers-Kronig transform. This study also shows that there is an excellent correspondence between the behavior of the predicted higher harmonics using the previously established theory of quasiparticle tunnel current in superconducting tunnel junctions by J.R. Tucker and M.J. Feldman and the measurements presented in this paper.
Low βc tunnel junctions have current-voltage characteristics which deviate from the intrinsic quasiparticle characteristic because of the ac Josephson effect. This effect has previously been analyzed for the special case of a pointlike junction in zero applied field. We demonstrate that deviations still occur when the critical current is suppressed by an applied field to a small fraction of its zero field value. The effects are significant for junctions whose length l is comparable to the Josephson penetration length λJ. These are often the junctions of practical interest. We present a simple model to explain the physical origin of these deviations, and also present detailed computer simulations using up to nine segments to model the distributed junction. For l = λJ, and an applied magnetic field which corresponds to the first minimum of the junction threshold characteristic, we find time-averaged voltages which deviate from the quasiparticle characteristic by up to 5%. Their magnitude is proportional to (l/λJ)2 and inversely proportional to the square of the applied field. This dependence can be used experimentally to confirm the observation of the effect.
A previously published analysis of the magnetic field variation of the reflected microwave power from small unbiased Pb-O-Pb Josephson junctions found strong temperature dependences for the basic tunnel parameters. We reanalyze those measurements employing independent variables, compensating for spurious external reflections, and accounting for noise reduction of the dc critical current. The cosφ amplitude ζ is positive near Tc and becomes negative at lower temperatures. In contrast to the previous work ζ is less sharply peaked, the junction rf resistance varies smoothly, and the capacitance is temperature independent. Our results clearly disagree with recent theoretical work.
The influence of microwave phase noise on rf-induced constant voltage steps generated by the ac Josephson effect is studied. Different circuit models for the junction excitation are considered: dc and rf voltage generators, dc and rf current generators, dc current and rf voltage generators. The analysis has been carried out assuming a power and band limited phase noise modulation in the first two cases, while in the last one a white frequency modulation spectrum is required for a treatment based on the Fokker-Planck equation. Some experimental results are reported, in order to display the basic phenomenological behavior.