Josephson current in carbon nanotubes with spin-orbit interaction

TL;DR

This paper explores how curvature-induced spin-orbit coupling affects the Josephson current in carbon nanotubes, revealing a tunable 0- transition influenced by magnetic fields and electron interactions.

Contribution

It provides a detailed analysis of the 0- transition in carbon nanotube Josephson junctions considering spin-orbit effects, magnetic fields, and electron interactions, with analytical phase boundaries.

Findings

Spin-orbit coupling induces a 0- transition in Josephson current.

Magnetic field tuning near orbital degeneracy controls the transition.

The 0 phase dominates in the Kondo regime.

Abstract

We demonstrate that curvature-induced spin-orbit (SO) coupling induces a $0-\pi$ transition in the Josephson current through a carbon nanotube quantum dot coupled to superconducting leads. In the non-interacting regime, the transition can be tuned by applying parallel magnetic field near the critical field where orbital states become degenerate. Moreover, the interplay between charging and SO effects in the Coulomb Blockade and cotunneling regimes leads to a rich phase diagram with well-defined (analytical) boundaries in parameter space. Finally, the 0 phase always prevails in the Kondo regime. Our calculations are relevant in view of recent experimental advances in transport through ultra-clean carbon nanotubes.