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Harmonic and reactive behavior of the quasiparticle tunnel current in SIS junctions

Hawal Rashid, Vincent Desmaris, Alexey Pavolotsky, Victor Y. Belitsky

Published Apr 1, 2016• 5 citations
Publisher

Abstract

In this paper, we show theoretically and experimentally that the reactive quasiparticle tunnel current of the superconductor tunnel junction could be directly measured at specific bias voltages for the higher harmonics of the quasiparticle tunnel current. We used the theory of quasiparticle tunneling to study the higher harmonics of the quasiparticle tunnel current in superconducting tunnel junction in the presence of rf irradiation. The impact of the reactive current on the harmonic behavior of the quasiparticle tunnel current was carefully studied by implementing a practical model with four parameters to model the dc I-V characteristics of the superconducting tunnel junction. The measured reactive current at the specific bias voltage is in good agreement with our theoretically calculated reactive current through the Kramers-Kronig transform. This study also shows that there is an excellent correspondence between the behavior of the predicted higher harmonics using the previously established theory of quasiparticle tunnel current in superconducting tunnel junctions by J.R. Tucker and M.J. Feldman and the measurements presented in this paper.

DOI
10.1063/1.4947133

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In this paper, we show theoretically and experimentally that the reactive quasiparticle tunnel current of the superconductor tunnel junction could be directly measured at specific bias voltages for the higher harmonics of the quasiparticle tunnel current. We used the theory of quasiparticle tunneling to study the higher harmonics of the quasiparticle tunnel current in superconducting tunnel junction in the presence of rf irradiation. The impact of the reactive current on the harmonic behavior of the quasiparticle tunnel current was carefully studied by implementing a practical model with four parameters to model the dc I-V characteristics of the superconducting tunnel junction. The measured reactive current at the specific bias voltage is in good agreement with our theoretically calculated reactive current through the Kramers-Kronig transform. This study also shows that there is an excellent correspondence between the behavior of the predicted higher harmonics using the previously established theory of quasiparticle tunnel current in superconducting tunnel junctions by J.R. Tucker and M.J. Feldman and the measurements presented in this paper.
The microwave response of the dc quasiparticle tunneling current in Josephson tunnel junctions, where the Josephson current is suppressed by an external magnetic field, has been studied quantitatively in order to clarify its characteristics as a probe for the measurement of the junction capacitance. Extensive experiments for both small and long junctions are carried out for distinguishing between microwave behaviors of lumped and distributed constant junctions. It is shown that the observed voltage dependence of the dc quasiparticle tunneling current modified by an applied rf field is in good agreement with a theoretical result which takes into account the influence of the microwave circuit connected to the junction. The comparison between theory and experiment gives the magnitude of the internal rf field in the junction. Together with the applied rf field, this internal rf field leads to the junction rf impedance which is dominated by the junction capacitance in our experimental condition. In the case of lumped junctions, this experimental rf impedance is in reasonable agreement with the theoretical one with the junction capacitance estimated from the Fiske step of the distributed junction fabricated on the same substrate; the obtained ratio of the experimental impedance to the theoretical one is approximately 0.6–1.7. In the case of distributed junctions, however, experimental values of their characteristic impedances are approximately 0.2–0.3 of theoretical values calculated by assuming the one-dimensional junction model and taking account of the standing-wave effect in the junction.
We have made the first direct measurement of the quantum susceptance that arises from the nondissipative part of quasiparticle tunneling in a superconductor-insulator-superconductor tunnel junction. The junction is coupled to an antenna and a superconducting microstrip stub to form a resonator; the resonant frequency is determined from the response of the junction to broadband radiation from a Fourier-transform spectrometer. A 19% shift of the resonant frequency, from 73 to 87 GHz, is observed, which arises from the change of the quantum susceptance of the junction with dc bias voltage. This shift is in excellent agreement with calculations based on the Werthamer-Tucker theory, which includes the quantum susceptance. We also demonstrate that it is essential to include the quantum susceptance in our theoretical computation to explain the photon-assisted-tunneling steps, which have negative dynamic conductance. Such steps are observed when the junction is pumped at slightly below the resonant frequency of the capacitor and the stub. The quantum susceptance should exist in all tunnel devices whose nonlinear I-V characteristics are due to elastic tunneling.
A harmonic Newton technique has successfully been used in the simulation of superconducting quasiparticle mixers in a five-port model. The steady-state large-signal waveform impressed across the tunnel junction by the incident local oscillator (LO) power is computed in the frequency domain. The three-frequency approximation provides the initial trial solution, which, together with the superlinear convergence property of Newton's method, ensures rapid convergence. A wide range of simulations based on the response function of a real superconductor-insulator-superconductor (SIS) junction is presented. The case of an SIS harmonic mixer (n=2) is also studied. Using a five-port model, the simulation explicitly takes the effect of the first harmonic into account. The algorithm and the principal results obtained for a hypothetical mixer incorporating the measured current-voltage characteristics of a real (SIS) junction are presented. The first results indicate that harmonic quasiparticle mixing may be very attractive in the submillimeter-wave band.>
We present a quantitative study of the current-voltage characteristics (CVC) of diffusive superconductor/insulator/ferromagnet/superconductor (SIFS) tunnel Josephson junctions. In order to obtain the CVC we calculate the density of states (DOS) in the F/S bilayer for arbitrary length of the ferromagnetic layer, using quasiclassical theory. For a ferromagnetic layer thickness larger than the characteristic penetration depth of the superconducting condensate into the F layer, we find an analytical expression which agrees with the DOS obtained from a self-consistent numerical method. We discuss general properties of the DOS and its dependence on the parameters of the ferromagnetic layer. In particular we focus our analysis on the DOS oscillations at the Fermi energy. Using the numerically obtained DOS we calculate the corresponding CVC and discuss their properties. Finally, we use CVC to calculate the macroscopic quantum tunneling (MQT) escape rate for the current biased SIFS junctions by taking into account the dissipative correction due to the quasiparticle tunneling. We show that the influence of the quasiparticle dissipation on the macroscopic quantum dynamics of SIFS junctions is small, which is an advantage of SIFS junctions for superconducting qubits applications.