Theory of planar quasi-ballistic Josephson junctions

TL;DR

This paper develops a quasiclassical theoretical framework for planar quasi-ballistic Josephson junctions, explaining experimental phenomena and revealing strong coupling effects in multi-terminal configurations.

Contribution

It introduces a novel theoretical approach based on Eilenberger equations to model quasi-ballistic Josephson junctions, accounting for surface and impurity reflections, and explains complex multi-terminal behaviors.

Findings

Critical current depends non-monotonically on interlayer length.

Multi-terminal junctions exhibit strong coupling effects.

Theory aligns with experimental observations.

Abstract

We develop a theoretical framework for planar quasi-ballistic Josephson junctions, where multiple superconducting leads are coupled through a large, nearly ballistic normal metal crystal. Our approach, based on quasiclassical Eilenberger equations, accounts for the dominant role of electron reflections from the crystal surfaces or single impurities, a mechanism distinct from both purely ballistic and diffusive limits. We calculate the critical current between superconducting leads for various geometries, examining its dependence on temperature and magnetic field. Crucially, we demonstrate that in multi-terminal setups, the junctions are not independent but form a strongly coupled system. The theory successfully explains key experimental observations from a companion work, including a non-monotonic dependence of the critical current on the interlayer length, providing a foundation for designing and understanding complex multi-terminal Josephson systems.