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Flux quantization for a superconducting ring in the shape of a Möbius band

We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a Möbius band, one using direct study of the Schrödinger 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 $Φ_0=hc/(2e)$. 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.