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Journal of Applied Physics

rf impedance of superconducting weak links

F. Auracher, T. Van Duzer

Published Feb 1, 1973• 77 citations
Publisher

Abstract

The rf impedance of a superconducting weak link with negligible capacitance is calculated for a variety of operating conditions. It is shown that the impedance is always real between harmonic steps of the I-V characteristic. The real part of the impedance is negative under certain conditions of bias for small rf signals, thus indicating the region of self-oscillation of the weak link.

DOI
10.1063/1.1662270

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The rf impedance of a superconducting weak link with negligible capacitance is calculated for a variety of operating conditions. It is shown that the impedance is always real between harmonic steps of the I-V characteristic. The real part of the impedance is negative under certain conditions of bias for small rf signals, thus indicating the region of self-oscillation of the weak link.
Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.
An experimental method to measure the imaginary and real part of the input impedance of an rf biased SQUID is described. The experimental results are in good agreement with the predictions of a detailed theoretical model of the rf SQUID, recently published. In particular it seems confirmed that the real part of the input impedance has a negative value which depends on the square of the input signal frequency. This effect must be taken into account whenever a SQUID is used to measure high frequency signals.
Measurements at 3 GHz of the microwave properties of a superconducting thin-film microbridge coupled to a narrowly tuned strip-line resonator (coupled Q approximately 10 3 ) indicate that such a device displays the same variations in small-signal impedance as predicted by the resistively shunted junction model of a Josephson weak-link. Whenever this impedance becomes negative the microbridge is found to generate microwave radiation whose frequency is determined not by the junction bias voltage but by the natural resonance of the strip-line.
We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.
A simple method is developed for analysis of the RF SQUID in regime, where the bias frequency ω is comparable to the natural R/L frequency of the SQUID ring. The input impedance of the RF SQUID is calculated for various values of the parametersq = \omega L/R\leq \leq \pi/4, signal frequency and detuning of the rf bias frequency from tank circuit resonant frequency. It is shown, that both the input resistance and the input inductance may be positive or negative. Measurement of the real part of the input impedance of a hysteretic RF SQUID are described. The experimental data are in qualitative agreement with the prediction of the theory.