Feynman Paradox about the Josephson effect and a sawtooth current in the double junction

TL;DR

This paper critically examines the Feynman approach to the Josephson effect, showing its limitations in explaining the DC effect and introducing coupled Ginzburg-Landau equations that reveal nonlinear coupling effects leading to a sawtooth current pattern in double junctions.

Contribution

It derives coupled Ginzburg-Landau equations from BCS theory, highlighting the importance of nonlinear coupling in explaining the DC Josephson effect and sawtooth current patterns.

Findings

Feynman approach fails to produce the DC Josephson effect.

Coupled Ginzburg-Landau equations reveal nonlinear coupling effects.

Sawtooth current pattern in double junctions emerges from the new model.

Abstract

We revisit the Feynman approach to the Josephson effect, which employs a pair of linear coupling equations for its modeling. It is found that while the exact solutions can account for the AC Josephson effect when the coupling strength is significantly less than the voltage, they fail to produce the DC Josephson effect in any practical scenario. To address this fundamental discrepancy, we derive the coupled Ginzburg-Landau (GL) equations for two interconnected superconductors based on BCS theory. These equations reveal that the nonlinear coupling, which is overlooked in the Feynman method, is crucial in describing the spontaneous symmetry breaking in superconductors, a critical factor for achieving the DC Josephson effect. When the coupled GL equations are applied to a double junction, a sawtooth current pattern emerges, a result unattainable via the Feynman approach.