Finite-Voltage Behavior of Lead-Copper-Lead Junctions

Abstract

Pb-Cu-Pb junctions were made by evaporating successively on to a glass substrate a strip of Pb, a disk of Cu, and a second strip of Pb at right angles to the first. Each Pb strip had a width $w$. At liquid-${\mathrm{He}}^4$ temperatures, the junctions could sustain a dc Josephson supercurrent less than or equal to the critical current $i_c$. When $i_c$ was small enough so that the Josephson penetration depth ${\lambda }_J \left(\propto i_c^{-\frac{1}{2}}\right)$ was greater than $\frac{1}{4}w$, the supercurrent flowed uniformly through the junction, which was said to be "weak." When $i_c$ was higher so that ${\lambda }_J$ was less than $\frac{1}{4}w$, the supercurrents were nonuniform, and the junction was said to be "strong." At a current $i$ greater than $i_c$, the voltage $v$ across a weak junction was in reasonable agreement with the theoretical result $v={(i^2-i_c^2)}^{\frac{1}{2}}R$, where $R$ is the normal-state resistance of the Cu film. For strong junctions, a dc supercurrent appeared at finite voltages, because the ac supercurrents had a nonzero time average. The experimental results are in good qualitative agreement with calculations on a one-dimensional model. When the current was fed into the junction asymmetrically, that is, when it was applied to one end of each Pb strip, the selffield of the current generated periodic structure on the $i-v$ characteristic, the period being typically 3 mA. The structure vanished if the currents were applied symmetrically, that is, the input and output currents divided equally between the ends of each lead strip. The application to a junction of rf electromagnetic radiation of angular frequency $\Omega$ induced constantvoltage current steps at voltages $\frac{\left(\frac{n}{m}\right)\hslash \Omega }{\mathrm{}\left(2e\right)\mathrm{}}$, where $n$ and $m$ are integers. The amplitude of the steps was modulated by the amplitude of the rf power and by a magnetic field in approximately the manner observed in tunnel junctions with oxide barriers. The dynamic resistance of the steps was less than 1.7 × ${10}^{-14\mathrm{}}$ $\Omega$. The electrochemical potential across the junction at which a given step appeared was not affected by either junction material or experimental conditions at a precision of 1 part in ${10}^8$. The highest frequency at which steps were induced was 2 MHz. At this frequency the skin depth of the copper was much less than $w$, and little radiation was coupled into the junction. The lowest frequency was 5 kHz, corresponding to a first-order induced step at about ${10}^{-11\mathrm{}}$ V. At this voltage, the Johnson-noise broadening of the Josephson frequency was also about 5 kHz. At lower frequencies, the noise completely destroyed the synchronization between the Josephson ac supercurrents and the rf radiation, so that no steps were observed.