# Geometric Phase and Superconducting Flux Quantization

## TL;DR

This paper explains the flux quantization in superconducting rings with mixed s-wave and d-wave materials as a geometric phase effect, revealing a fundamental quantum mechanical origin for the phase shift.

## Contribution

It provides a geometric phase interpretation of flux quantization phenomena in hetero-junction superconductors with s-wave and d-wave pairing.

## Key findings

- Flux quantization in d-wave interrupted rings is due to geometric phase discontinuity.
- The phase shift of π is a fundamental quantum mechanical consequence.
- The reinterpretation unifies flux quantization with geometric phase theory.

## Abstract

In a ring of s-wave superconducting material the magnetic flux is quantized in units of $\Phi_0 = \frac{h}{2e}$. It is well known from the theory of Josephson junctions that if the ring is interrupted with a piece of d-wave material, then the flux is quantized in one-half of those units due to a additional phase shift of $\pi$. We reinterpret this phenomenon in terms of geometric phase. We consider an idealized hetero-junction superconductor with pure s-wave and pure d-wave electron pairs. We find, for this idealized configuration, that the phase shift of $\pi$ follows from the discontinuity in the geometric phase and is thus a fundamental consequence of quantum mechanics.

---
Source: https://tomesphere.com/paper/0704.0803