Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

Microwave impedance of superconducting weak links

J. D. Franson, James E. Mercereau

Published Jul 1, 1976• 17 citations
Publisher

Abstract

Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.

DOI
10.1063/1.323124

Related papers

Microwave impedance measurements of point-contact Josephson weak links

P. F. Michelson, R. P. Giffard

We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.

IEEE Transactions on Magnetics•Jan 1, 1981•0 citations

I. The phase-current relation at zero voltage in proximity effect bridges. II. The interaction of proximity effect bridges with superconducting microstrip resonators

Tomas Ganz

Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.

•Jan 1, 1976•0 citations

Capacitance measurement of Josephson tunnel junctions with microwave-induced dc quasiparticle tunneling currents

K. Hamasaki, Keiji Yoshida, F. Irie +1 more

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.

Journal of Applied Physics•May 1, 1982•3 citations

Phase-locking and microwave impedance of Josephson junctions with linear-periodic current-phase relations

Norio Fujimaki, Yoji Okabe, Sogo Okamura

Some types of Josephson junctions such as long microbridges, S-N-S junctions, and junctions with a series palastic inductance are known to have nonsinusoidal current-phase relations which can be approximated by linear-periodic functions. In this paper the equivalent circuit equation of the resistively shunted junction model with linear-periodic current-phase relation is solved. The heights of zeroth and first constant-voltage steps in the I-V characteristics and the impedance at these steps are obtained analytically. This analysis shows that the impedance at the first step lies on a semicircle in the impedance plane with its center at the impedance of the zeroth step. The calculated impedance is compared with the experimental results by Claridge et al. The theory presented here can explain some features of experimental results which differ considerably from predictions based on a sinusoidal current-phase relation. Among these are the value of bias current corresponding to the center of the first step, and the appearance of ’’shoulders’’ in the imaginary part of the impedance at the first step.

Journal of Applied Physics•Jun 1, 1980•3 citations

Mixing in superconducting weak links : numerical calculations and experimental results

F. Auracher, T. Van Duzer

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.

Revue de Physique Appliquée•Jan 1, 1974•23 citations

Harmonic current-phase relation in Nb–Al-based superconductor/insulator/normal conductor/insulator/superconductor-type Josephson junctions between 4.2 K and the critical temperature

Martin Götz, Vladimir V. Khanin, H. Schulze +6 more

For a study of the supercurrent–phase relationship, we have fabricated Nb/Al/AlOx/Al/AlOx/Al/Nb-based Josephson junctions of low critical current density. At 4.2 K, junctions of a nominal area of 10×10 μm2 showed a nonhysteretic dc current–voltage characteristic with a critical current of about 10 μA. Similar junctions were part of washer-type rf superconductor quantum interference devices. These samples were inductively coupled to high-quality tank circuits for measurements at 4.2 K or at higher temperatures up to values close to the critical temperature of niobium. In this range, the current–phase relation, as deduced from impedance measurements of the phase-biased junction, did not deviate significantly from the sinusoidal shape.

Applied Physics Letters•Aug 28, 2000•5 citations
Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.
We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.
Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.
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.
Some types of Josephson junctions such as long microbridges, S-N-S junctions, and junctions with a series palastic inductance are known to have nonsinusoidal current-phase relations which can be approximated by linear-periodic functions. In this paper the equivalent circuit equation of the resistively shunted junction model with linear-periodic current-phase relation is solved. The heights of zeroth and first constant-voltage steps in the I-V characteristics and the impedance at these steps are obtained analytically. This analysis shows that the impedance at the first step lies on a semicircle in the impedance plane with its center at the impedance of the zeroth step. The calculated impedance is compared with the experimental results by Claridge et al. The theory presented here can explain some features of experimental results which differ considerably from predictions based on a sinusoidal current-phase relation. Among these are the value of bias current corresponding to the center of the first step, and the appearance of ’’shoulders’’ in the imaginary part of the impedance at the first step.
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.
For a study of the supercurrent–phase relationship, we have fabricated Nb/Al/AlOx/Al/AlOx/Al/Nb-based Josephson junctions of low critical current density. At 4.2 K, junctions of a nominal area of 10×10 μm2 showed a nonhysteretic dc current–voltage characteristic with a critical current of about 10 μA. Similar junctions were part of washer-type rf superconductor quantum interference devices. These samples were inductively coupled to high-quality tank circuits for measurements at 4.2 K or at higher temperatures up to values close to the critical temperature of niobium. In this range, the current–phase relation, as deduced from impedance measurements of the phase-biased junction, did not deviate significantly from the sinusoidal shape.