Josephson Weak Links: Two Models

Abstract

In 1968 Stewart¹ and McCumber² independently advanced a theory to explain why the observed current—voltage characteristics of one type of weak-link device differed so markedly from that of related devices. They proposed that the difference between the current—voltage characteristics of many of these devices could be explained by analyzing them in terms of a lumped circuit model that treated the distributed internal resistance and capacitance of the device as a single resistor and a single capacitor, both in parallel with a hypothetical idealized Josephson element having zero capacitance and an infinite resistance to quasiparticle tunneling. These ac and dc supercurrents obey Josephson’s equations³

$$i={{i}_{c}}\sin \varnothing $$

(1a)

and

$$\left( 2e/h \right)V=d\varnothing /dt$$

(1b)

where i _c is the critical supercurrent, ø and V are the pair-phase difference and instantaneous voltage across the element, and i is the instantaneous supercurrent. The observed time-averaged dc current—voltage characteristic of such a lumped circuit model is a function of the dimensionless parameter

$${{\beta }_{c}}=\left( 2e/h \right){{i}_{c}}\left( C/{{G}^{2}} \right)$$

(2)

which gives a normalized measure of the balance of influence of the capacitance C, shunt conductance G, and critical supercurrent i _c on the hysteresis.

This work was performed under the auspices of the U.S. Atomic Energy Commission. One of us (P.K.H.) was supported by a National Science Foundation Fellowship during the research.