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Journal of Applied Physics

Basic Josephson tunnel parameters at microwave frequency—A reassessment

M. J. Feldman, S. Rudner, T. Claeson

Published Sep 1, 1980• 5 citations
Publisher

Abstract

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.

DOI
10.1063/1.328357

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Basic Josephson tunnel parameters at microwave frequency—Strong temperature variations

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Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.

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N. F. Pedersen, J. Mygind, O. H. Soerensen +1 more

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Le Journal de Physique Colloques•Aug 1, 1978•3 citations
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.
Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.
We have studied the power dependence of the microwave-induced dc voltages across "unbiased" Pb---Pb oxide---Pb Josephson tunnel junctions and found a systematic dependence. We have also found that the Josephson effect in the form of induced quantum voltages was observable in a large dc magnetic field as high as 0.5 kG, about one-half of the Hc2{H}_{c2}Hc2​ of the superconducting Pb film.
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.