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Acta Physica Sinica

THE CURRENT STEPS IN SUPERCONDUCTING WEAKLINKS

YAO XI-XIAN, 南京大学物理系

Published Jan 1, 1979• 1 citation
Publisher

Abstract

In the presence of a battery source and a radiation field, a superconducting weaklink can be represented by a simplified model consisting of a resistance shunted Josephson junction driven by a constant current source. Using such a model, we give a general criterion for the occuring of constant voltage current steps in the current-voltage characteristics of the weaklink. Following this criterion, we have also discussed the absence of sub-harmonic current steps. For the case while the radiation field is very weak, the current step heights are calculated by pertubation method. The current step heights are also obtained by numerical compution for the case of strong field.

DOI
10.7498/aps.28.416

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In the presence of a battery source and a radiation field, a superconducting weaklink can be represented by a simplified model consisting of a resistance shunted Josephson junction driven by a constant current source. Using such a model, we give a general criterion for the occuring of constant voltage current steps in the current-voltage characteristics of the weaklink. Following this criterion, we have also discussed the absence of sub-harmonic current steps. For the case while the radiation field is very weak, the current step heights are calculated by pertubation method. The current step heights are also obtained by numerical compution for the case of strong field.
Abstract The method of numerical solution of equations is used within the resistive model to study the behavior of deviations of the current‒voltage characteristics of nonideal Josephson junctions from similar characteristics of ideal (standard) junctions. Nonideal Josephson junctions are those in which the current‒phase relation contains additional Josephson harmonics. The dependences of the amplitudes of current steps (Shapiro steps) on the power of external electromagnetic radiation is calculated. The shape of these dependences is shown to deviate from the corresponding dependences for ideal Josephson junctions. In addition, the paper examines the features of the occurrence of additional current steps on the current‒voltage characteristics of Josephson junctions and shows a possibility of their absence in the case of the presence of additional harmonics in the current‒phase relation. The obtained results prove that by analyzing the step structure of the current‒voltage characteristics it is possible to obtain information about the properties of Josephson junctions and superconductors that form them.
The current height of RF-induced voltage steps in nonhysteretic single Josephson junctions is usually a small fraction of the critical current. It is demonstrated that when a resistively shunted DC superconducting quantum interference device (SQUID) is subjected to an RF magnetic flux, a voltage step with a large current height is obtained. In contrast to weak selection rules for single Josephson junctions, strong selection of the step harmonic number occurs in a shunted DC SQUID for appropriate choice of RF amplitude and DC flux offset, with odd harmonic numbers selected by half-integer flux quantum offsets and even harmonic numbers by integer flux quantum offsets. This pronounced effect has immediate implications for voltage standards and fast, high-precision digital-to-analog converters.>
We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.
Abstract Josephson junctions based on superconducting materials are fundamental components for quantum detection, quantum communication and quantum computers. An accurate behavioral model of Josephson junctions is the prerequisite for predicting various superconducting circuits. In this study, We present a resistively and capacitively shunted junction (RCSJ) model-based behavioral-level model for the current-voltage characteristics of Josephson junctions. This model accurately predicts the current-voltage characteristics and their temperature dependencies of Josephson junctions made of different materials under three typical working modes: underdamped voltage-driven, overdamped current-driven, and underdamped current-driven. Additionally, it forecasts the critical current and superconducting energy gap characteristics with respect to temperature, as well as the constraint relationship between the shunt resistance, superconducting energy gap, and critical current. Comparing the measured data with the simulation predictions, the model has an average accuracy of 85.9%, which illustrates the reliability of the model.
For a current-driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high-frequency currents is calculated with a second-order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic-frequency regions depending on whether the internal self-generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0< or >ω the response could be expressed by easily observable parameters of the dc voltage-current characteristics. This permits comparison of the predictions with experimental results obtained on point-contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point-contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise-equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.