Semiclassical quantization of spinning quasiparticles in ballistic Josephson junctions

TL;DR

This paper develops a semiclassical framework to analyze the spectrum of Andreev bound states in ballistic Josephson junctions with magnetic materials, revealing how spin dynamics influence quantum states.

Contribution

It introduces a novel semiclassical quantization method based on an Andreev-Wilson loop, linking spin precession and magnetic phase shifts to bound state spectra in Josephson junctions.

Findings

Spectrum depends on spin angle mismatch

The Andreev-Wilson loop encodes spin and magnetic effects

Measurement of spin-resolved density of states reveals loop details

Abstract

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semi-classic limit. The spectrum of Andreev bound states is obtained from the single-valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position/particle-hole/spin space is constructed, and shown to depend on only two parameters, namely a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials.