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I. The phase-current relation at zero voltage in proximity effect bridges. II. The interaction of proximity effect bridges with superconducting microstrip resonators

Tomas Ganz

Published Jan 1, 1976• 0 citations
Publisher

Abstract

Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.

DOI
10.7907/n97w-bw02.

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IEEE Transactions on Magnetics•Mar 1, 1975•26 citations
Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum
interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges
were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were
seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized
Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed
self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating
Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.
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.
Josephson junctions connected to high Q microstriplines display current-steps which we attribute to standing wave resonances. The step voltages of the resonances depend on sample geometry and correspond to frequencies at which the loaded microstrip is resonant. The voltages of the resonances are insensitive to applied magnetic field and junction current density. Current step amplitudes scale with the zero-voltage critical current, and are largest for zero applied magnetic field. The strength of these resonant steps has important implications for biasing weakly damped Josephson junction circuits. In addition, the resonances are a useful tool for measuring microstrip properties.
Techniques have been developed with which it is possible to fabricate superconducting thin-film structures with a wide variety of electrical and superconducting parameters which show Josephson-like phenomena. These bridges-based on the proximity effect-are made in layered thin-film ``substrates'' using a large variety of superconducting and nonsuperconducting materials. In this paper we detail the fabrication techniques and the electrical and superconducting characteristics for these proximity effect bridges including a simple low-frequency (<10 GHz) equivalent circuit based on analysis and experiment which closely describes the quantum phase coherence operation of the bridges in their voltage sustaining state. Extension of these fabrication techniques to entire thin-film electrical circuits including resistors, capacitors, and inductors with these bridges and leading to an entire superconducting microcircuit technology is discussed.
The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental and numerical investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAl2O3Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field. The largest step corresponds to a superconducting phase difference of π between neighboring junctions.
Planar series arrays of up to 500 proximity effect superconducting bridges have been fabricated with sufficient uniformity to respond coherently to incident radiation (10-20,000MHz) without separate biasing. By varying the geometry, resistance for the arrays can range from .1-50Ω. Despite this high total impedance, low frequency coherent response to external radiation is limited only by single bridge voltage noise. Low frequency (30-500MHz) coherent internal voltage oscillations of current biased arrays have been detected and confirm that the oscillating voltage signal grows linearly in bridge number while the voltage noise increases only as the square root. An array of n elements responds to incident high frequency radiation in first approximation as though it were a simple Josephson junction but quantized in units of n(h/2e). Coincident operation to high frequency depends strongly on small (\leq 1\mu) bridge separation. High resistance, coincident operation, and exponential dependence of critical current on temperature make these arrays good candidates for voltage standards, coherent and bolometric radiation detectors, and cryogenic rf sources.