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Physical Review Letters

Effect of leads and energy gap upon the retrapping current of Josephson junctions

Alan T. Charlie Johnson, Christopher J. Lobb, M. Tinkham

Published Sep 1, 1990• 29 citations
Publisher

Abstract

We observe that the retrapping current of high-resistance, small-capacitance, superconducting tunnel junctions decreases sharply with decreasing temperature, and then has a puzzling, flat, nonzero minimum at low T, rather than continuing to decrease as quasiparticle damping freezes out. We explain the crossover by considering the combined admittance of the leads and of the junction (including the onset of pair-breaking tunneling at the gap voltage) at both dc and the Josephson frequency. Our analog simulations and analytic approximations both agree well with the data.

DOI
10.1103/physrevlett.65.1263

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We observe that the retrapping current of high-resistance, small-capacitance, superconducting tunnel junctions decreases sharply with decreasing temperature, and then has a puzzling, flat, nonzero minimum at low T, rather than continuing to decrease as quasiparticle damping freezes out. We explain the crossover by considering the combined admittance of the leads and of the junction (including the onset of pair-breaking tunneling at the gap voltage) at both dc and the Josephson frequency. Our analog simulations and analytic approximations both agree well with the data.
We present observations of charging effects for Cooper pairs in short linear arrays of small-capacitance Josephson junctions. Current-voltage characteristics show a Coulomb gap for Cooper-pair tunneling when the charging energy exceeds the Josephson coupling energy. In a double junction a zero-voltage current is observed that is modulated by a gate voltage applied to the metal island between the junctions. For longer arrays a crossover from Coulomb blockade of Cooper-pair tunneling to a supercurrent is observed when the ratio of Josephson coupling to charging energy is increased.
Measurements of temperature dependence of the return current in high quality Nb/AlOx/Nb Josephson junctions are presented. From the experimental data, we obtain the effective resistance, i.e., the effective dissipation, for the retrapping process, according to the generalized resistively shunted junction model proposed by Chen, Fisher, and Leggett. We present a careful analysis, based on a comparison between the measured temperature dependencies of both the return and the quasiparticle tunneling current. We find that the junction subgap conductance, which includes the quasiparticle and the quasiparticle-pair interference terms, is responsible for the return process. The measurements have been performed on various samples, in a wide range of critical current densities from 50 to 2250 A/cm2, covering different damping regimes and spanning over the high and low temperature limits. Junctions with low critical current density show ideal dissipation which makes the return current scale with temperature according to the BCS exponential behavior without flattening out effects. This result may be relevant for the possible use of Nb/AlOx/Nb junctions in macroscopic quantum coherence experiments, which strongly require a very low dissipation.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
Within a semiclassical approximation and at the weak-coupling limit, where the charging energy dominates the Josephson coupling energy, the dynamics of small-capacitance superconducting tunnel junctions can be described by a stochastic master equation for the probability distribution of junction charges. We develop a method of solving this equation and obtain an analytic solution when Cooper-pair, quasiparticle, and Zener tunneling are all present under an arbitrary Ohmic conductance at zero temperature. We use this solution to systematically investigate the static and dynamic properties of small Josephson junctions. The charge distributions, current-voltage characteristics, and voltage spectra are analytically calculated and numerically evaluated for wide ranges of parameters. The separate contributions from quasiparticle and Cooper-pair tunneling to voltage spectra are evaluated and compared based on their respective sum rules. The linewidths of the resonance peaks for single-electron tunneling and Bloch oscillations are also discussed.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.
Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.