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Physical review. B, Condensed matter

Quantum susceptance and its effects on the high-frequency response of superconducting tunnel junctions

Qing Hu, C. A. Mears, P. L. Richards, Frances L. Lloyd

Published Dec 1, 1990• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.42.10250

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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.
We have measured the linear response of the quasiparticle current in a Nb/AlOx/Nb junction from 75–200 GHz. Picosecond pulses of millimeter wave radiation were generated by illuminating a photoconductive switch with a mode-locked laser. The pulses were coupled to the junction through an impedance-mismatched, planar lithographed antenna. The broadband response of the superconductor-insulator-superconductor junction was measured by monitoring changes in the dc current induced by interfering two electrical pulses at the junction as a function of the time delay between them. The data are in agreement with the linear theory of photon-assisted tunneling.
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.
In this paper, we present an investigation of the contribution of quantum susceptance in capacitance measurements of superconductor-insulator-superconductor tunnel junctions. We directly measured the one-port S-parameter S11by utilizing a 4-K probe station in combination with a network analyzer. We observed a bias voltage dependence of the measured junction susceptance which demonstrates the contribution of quantum susceptance. Calculation results performed, based on a simple equivalent circuit model, were in excellent agreement with the measurements. Experiment and analysis methods suggested here enable the quantitative verification of the contribution of quantum susceptance and are an effective way of extracting the junction's geometric capacitance.
We report the first observations of photon-assisted quasiparticle tunneling and AC Josephson effect in superconducting tunnel junctions irradiated with far-infrared (FIR) radiation. Radiation at 246 GHz (λ=1.22 mm) and 604 GHz (496 μm) from an optically-pumped FIR laser source was used. Tin-tin oxide-lead junctions of ∼1 (μm)2area were fabricated on crystal quartz substrates with integral planar dipole antennas of resonant length at the frequency of the incident radiation. The observed photon-assisted tunneling features are in excellent agreement with the Tien-Gordon theory, and the inferred responsivity approaches the quantum limit at low temperatures for photon energies less than the gap. At 604 GHz, with a 176 ohm junction, we have seen 7 Josephson steps, comparable to point contact performance. The variation of the step widths with laser power is found to agree quite well with both the RSJ model and the Werthamer theory. For low resistance junctions (e.g. 16 ohms), we find the Josephson steps to be flat and to agree well with the shape predicted by the RSJ model without noise rounding, while noise rounding is very evident with the higher resistance junctions. In all cases, the step shape is in reasonable agreement with the theory of P. A. Lee, using a noise temperature of 10-20K with an appropriate small junction capacitance.
The strong nonlinearity of the quasiparticle tunneling current in superconductor-insulator-superconductor junctions near the full-gap voltage 2Δ/e can be used for direct detection of microwave signals. Measurements at 36 GHz yielded a current responsivity of 3500 A/W, which is within a factor of 2 of the quantum-limited value e/∇ω. The measured NEP of 2.6±0.8×10−16 W/,Hz1/2 is the lowest value reported to date and can probably be improved significantly. The experimental results are compared with both the standard classical analysis and photon-assisted tunneling theory.
A detailed analysis of the effects of the quantum susceptance on the performance of superconductor-insulator-superconductor (SIS) mixers is performed. It is found that the principal effects of the quantum susceptance are to change the DC bias at which optimum coupling of the signal to the mixer occurs, and to change the output admittance at the IF frequency, thus changing the available gain. It is shown that at the signal port the principal effect is to change the bias voltage at which optimum coupling to the mixer occurs. A more dramatic effect occurs at the IF port, where the quantum susceptance leads to negative values of the output conductance, which causes the available gain to be infinite.