Flux quantization for a superconducting ring in the shape of a M\"obius band

TL;DR

This paper demonstrates that magnetic flux in a superconducting M"obius band ring is quantized in integral or half-integral multiples of the flux quantum, using Schr"odinger equation analysis and gauge bundle holonomy, with experimental relevance.

Contribution

It provides two theoretical derivations of flux quantization in a M"obius superconducting ring, highlighting the possibility of half-integer quantization in nodal states.

Findings

Flux quantization in integral or half-integral multiples of .

Half-integer quantization occurs in nodal states with wavefunction vanishing at the center.

Experimental evidence supports the existence of nodal states with half-integer flux quantization.

Abstract

We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a M\"obius band, one using direct study of the Schr\"odinger equation and the other using the holonomy of flat U(1)-gauge bundles. Both methods show that the magnetic flux must be quantized in integral or half-integral multiples of $\Phi_0=hc/(2e)$. Half-integral quantization shows up in "nodal states" whose wavefunction vanishes along the center of the ring, for which there is now some experimental evidence.