Casimir-Josephson force on a point contact between two superconductors

TL;DR

This paper derives the Casimir-Josephson force on a point contact between two superconductors, highlighting the dominant role of quantum fluctuations outside the gap and its relation to the electromagnetic Casimir effect.

Contribution

It provides a new calculation of the superconducting Casimir-Josephson force including contributions from the continuous spectrum, extending previous work focused on discrete Andreev levels.

Findings

Force depends logarithmically on contact length and phase difference.

Quantum fluctuations outside the gap dominate the force.

Comparison with earlier models shows the importance of continuous spectrum contributions.

Abstract

We calculate the elongation or contraction force $F$ on a point contact (length $L$) connecting two superconductors with a phase difference $\phi$. When $L$ is small compared to the superconducting coherence length $\xi_0$ this force is given by $F=-(\Delta_0/\pi\xi_0)\ln(\xi_0/L)\cos\phi$ per spin-degenerate transverse mode. Quantum fluctuations in states from the continuous spectrum outside the superconducting gap $\Delta_0$ give the dominant contribution to this force, which may be understood as the superconducting counterpart of the electromagnetic Casimir force. We compare with earlier work that only included contributions from the discrete spectrum of Andreev levels.