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Journal of Applied Physics

Current-voltage characteristics of low βc tunnel junctions with magnetically suppressed critical currents

L. N. Smith, D. W. Jillie

Published Aug 1, 1981• 1 citation
Publisher

Abstract

Low βc tunnel junctions have current-voltage characteristics which deviate from the intrinsic quasiparticle characteristic because of the ac Josephson effect. This effect has previously been analyzed for the special case of a pointlike junction in zero applied field. We demonstrate that deviations still occur when the critical current is suppressed by an applied field to a small fraction of its zero field value. The effects are significant for junctions whose length l is comparable to the Josephson penetration length λJ. These are often the junctions of practical interest. We present a simple model to explain the physical origin of these deviations, and also present detailed computer simulations using up to nine segments to model the distributed junction. For l = λJ, and an applied magnetic field which corresponds to the first minimum of the junction threshold characteristic, we find time-averaged voltages which deviate from the quasiparticle characteristic by up to 5%. Their magnitude is proportional to (l/λJ)2 and inversely proportional to the square of the applied field. This dependence can be used experimentally to confirm the observation of the effect.

DOI
10.1063/1.329382

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Low βc tunnel junctions have current-voltage characteristics which deviate from the intrinsic quasiparticle characteristic because of the ac Josephson effect. This effect has previously been analyzed for the special case of a pointlike junction in zero applied field. We demonstrate that deviations still occur when the critical current is suppressed by an applied field to a small fraction of its zero field value. The effects are significant for junctions whose length l is comparable to the Josephson penetration length λJ. These are often the junctions of practical interest. We present a simple model to explain the physical origin of these deviations, and also present detailed computer simulations using up to nine segments to model the distributed junction. For l = λJ, and an applied magnetic field which corresponds to the first minimum of the junction threshold characteristic, we find time-averaged voltages which deviate from the quasiparticle characteristic by up to 5%. Their magnitude is proportional to (l/λJ)2 and inversely proportional to the square of the applied field. This dependence can be used experimentally to confirm the observation of the effect.
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 studied the current-voltage characteristics of small area tunnel junctions at temperatures below 1 K. The junctions were made in an edge geometry with a Nb base electrode and had areas less than .05 μm2and critical currents in the nA range. Although the measured I-V characteristics resemble those of ordinary hysteretic junctions, the supposed zero-voltage portion of the curve proved to have a finite slope and to deviate from zero voltage. For these junctions it is apparently possible for occasional 2π phase slips to occur without switching to the usual voltage state. This behavior can be explained either by macroscopic quantum tunneling or by a model in which the effective shunt conductance of the junction is frequency dependent.
Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration ppp are considered, where pc{p}_{c}pc​ is the percolation threshold. For p>pcp>{p}_{c}p>pc​ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At pc{p}_{c}pc​ and finite temperature T,T,T, the results show the scaling behavior of a T=0T=0T=0 superconducting transition. The resistance is linear but vanishes for decreasing TTT with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted XY\mathrm{XY}XY model at pc.{p}_{c}.pc​.
The magnetic field dependence of the Josephson current of a Josephson tunnel junction whose shape was a normal distribution is analyzed for superconducting tunnel junction (STJ) photon detector applications. It was found that the Josephson current of a normal distribution junction is very sensitive to the external magnetic field and follows a function of exp (-B 2), while a conventional rectangular STJ exhibits the well-known Fraunhofer pattern of sin x/x. Numerical calculations show that the Josephson current of the normal distribution junction can be suppressed by an external magnetic field that is one tenth of that needed for conventional rectangular junctions. Calculations of a normal distribution junction approximated with a 1 µm mesh also show that the Josephson current is sufficiently suppressed by a small magnetic field. The effect of the misalignment of the angle between the junction and the magnetic field was evaluated. It was found that for a normal-distribution-shaped junction, misalignment of the magnetic field is allowed within ± 5°, suppressing the Josephson effect by two orders of magnitude more than that of a rectangular junction.
Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.