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Journal of Physics Conference Series

Dynamics of underdamped Josephson junctions with nonsinusoidal current-phase relation

Victor K. Kornev, T. Yu. Karminskaya, Yu. V. Kislinskiĭ, P.V. Komissinki, K. Y. Constantinian, G. A. Ovsyannikov

Published Jun 1, 2006• 10 citations
Publisher

Abstract

Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.

DOI
10.1088/1742-6596/43/1/269

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Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.
Josephson junction, as the core nonlinear element underpinning superconducting electronics, is characterized by its current-phase relation (CPR), which fundamentally determines the dynamical properties and functional capabilities of superconducting quantum devices. Traditional Josephson junctions typically exhibit a traditional sinusoidal CPR; however, the junctions characterized by non-sinusoidal CPR have recently attracted considerable attention due to their distinctive physical properties and promising quantum device applications. In this work, a numerical model tailored specifically for junctions exhibiting non-sinusoidal CPR is developed by integrating experimentally measured current-voltage (I-V ) characteristics from Nb/Al-AlOx/Nb junctions into a resistively and capacitively shunted junction (RCSJ) framework. By leveraging this refined model, the influence of CPR skewness on Josephson junction dynamics is systematically investigated. Our results indicate that in underdamped junctions, the critical current significantly diminishes with the increase of CPR skewness, a behavior reminiscent of the adjustable critical currents typically observed in DC superconducting quantum interference devices (SQUIDs). Conversely, in overdamped junctions, the influence of CPR skewness on the I-V characteristics is found to be negligible. However, our numerical simulations under microwave irradiation indicate that nonsinusoidal CPRs readily promote the emergence of half-integer Shapiro steps in overdamped junctions, thereby establishing CPR skewness as a plausible microscopic origin for this phenomenon. In addition, the advanced design system (ADS) simulations is employed to model nonlinear resonators and DC SQUID circuits, offering a detailed investigation into how nonsinusoidal CPRs modulate the Josephson inductance and magnetic flux response. Our findings reveal that engineering the CPR of Josephson junctions provides substantial flexibility in the design of superconducting qubits, parametric amplifiers, and non-magnetic nonreciprocal devices. This tunability underscores significant opportunities for developing next-generation superconducting electronic components. The Josephson junctions with engineered CPR offer expanded functionality for superconducting quantum technologies. This study suggests that customized CPR can enhance control over the dynamical behavior of junctions, and promote the optimized designs of superconducting qubits, parametric amplifiers, and nonmagnetic nonreciprocal devices.
The electrophysical and dynamic parameters (Shapiro steps and detector response) of hybrid heterostructures based on oxide superconductors with the d -wave symmetry of the order parameter are studied. Deviation of the current-phase relation from the trivial (sinusoidal) form is revealed. It is shown in terms of a generalized Resistive Shunted Function model with the junction capacitance and higher harmonics of the current-phase relation has virtually no influence on the width of harmonic Shapiro steps but changes the scale of the step-width dependence on the ac current of an external electromagnetic field. In addition, it is shown that these dependences have no local minima if the current-phase relation (CPR) contains harmonics higher than the first. For heterostructures, the amplitudes and signs of the CPR harmonics are determined through comparison of theoretical and experimental data.
An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed.
Integer and half-integer Shapiro step amplitudes in the current-voltage characteristics of symmetric superconducting quantum interference devices (SQUIDS), containing more than one Josephson junction on each arm, are analytically calculated for small values of the parameter β and in the absence of noise. This analysis is made possible by the reduction of the dynamical equations of the multiple-junction SQUID to the dynamical equation of a single Josephson junction possessing a nonconventional current-phase relation.
We report on measurements of dc electron transport and microwave dynamics of thin film hybrid Josephson junctions with an oxide antiferromagnetic interlayer. The base superconducting electrode YBaCuO and the antiferromagnetic (AF) interlayer CaSrCuO (with thickness d = 20 – 70 nm) were grown by laser ablation on NdGaO 3 substrates. I-V curves were well fitted to RSJ model and had no excess current, I C R N products were of order 0.2 mV at T =4.2 K. We did not observe any noticeable reduction of I C R N with increasing d . Such "tunnellike" behaviour also resulted in appearance of singularities on I-V curve when magnetic field was applied. Oscillating with microwave power integer and half-integer Shapiro steps were registered along with sub-harmonic detector response. Moreover, for some of junctions a "devil" staircase structure was observed on I-V curves and giant noise-like signals were measured in 1-2 GHz band at the certain levels of microwave power. Observed features, noise performance and the impact of the second harmonic in current-phase relation on junction dynamics are discussed taking into account data for structures without AF interlayer.