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Soviet Journal of Low Temperature Physics

Quantum interference and the characteristics of Josephson junctions

V. I. Shnyrkov, V. A. Khlus, Georgy M. Tsoi, M. P. Chetaev

Published Jun 1, 1978• 0 citations
Publisher

Abstract

A single-junction superconducting quantum interferometer with external high-frequency excitation is considered, in which the weak coupling is described within the framework of the resistive model. An analysis for the hysteresis-free state serves to define the parameters characterizing the Josephson junction, including the current as a function of the phase difference at the junction, as well as the interference term in the dissipative component of the current. The theoretical results are compared with experiment to define certain parameters of the Josephson junction and the sign of the interference term.

DOI
10.1063/10.0029694

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A single-junction superconducting quantum interferometer with external high-frequency excitation is considered, in which the weak coupling is described within the framework of the resistive model. An analysis for the hysteresis-free state serves to define the parameters characterizing the Josephson junction, including the current as a function of the phase difference at the junction, as well as the interference term in the dissipative component of the current. The theoretical results are compared with experiment to define certain parameters of the Josephson junction and the sign of the interference term.
The theory of self-induced resonances in asymmetric two-junction interferometer device is presented. In real devices, it is impossible to have an ideal interferometer free of imperfections. Thus, we extended previous theoretical approaches, introducing a model that contains several asymmetries: Josephson current ϵϵϵ, capacitances $\ensuremath{\chi}$, and dissipation $\ensuremath{\rho}$ presented in an equivalent circuit. Moreover, nonconventional symmetry of the order parameter in high temperature superconducting quantum interference devices forced us to include phase asymmetries. Therefore, the model has been extended to the case of $\ensuremath{\pi}$-shift interferometers, where a phase shift is present in one of the junctions.
The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.
Partly resistive superconducting quantum interference devices (RSQUIDs) are used in noise thermometry in the liquid helium temperature range. Here we analyze one type of RSQUID that has not been thoroughly investigated until now: the direct current biased with two Josephson junctions and a resistive part connected in series with the junctions and closed by a superconducting ring. The resistive shunted model of the Josephson junctions is used for the analysis. Two cases of the RSQUID ring inductance were analyzed: (i) negligibly small and (ii) small but finite inductance. The expressions for the low frequency output signal, the current–voltage (I–V) characteristics, and the current flowing through the resistive part are obtained. In the dependence of the output frequency versus the dc current passed through the resistive part often an offset is observed experimentally. This phenomenon can be explained as an influence of an asymmetry in the critical currents of the junctions.
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
In addition to the usual superconducting current, Josephson junctions (JJs) support a phase-dependent conductance related to the retardation effect of tunneling quasi-particles. This introduces a dissipative current with a memory-resistive (memristive) character that should also affect the current noise. By means of the microscopic theory of tunnel junctions we compute the complete current autocorrelation function of a Josephson tunnel junction and show that this memristive component gives rise to both a previously noted phase-dependent thermal noise, and an undescribed non-stationary, phase-dependent dynamic noise. As experiments are approaching ranges in which these effects may be observed, we examine the form and magnitude of these processes. Their phase dependence can be realized experimentally as a hysteresis effect and may be used to probe defects present in JJ based qubits and in other superconducting electronics applications.