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

Abstract

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 ${\Phi }_0=hc/(2e)$. 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.

5 pages with 1 figure, improved figure and added 2 references and more discussion

References in corpus (2)

• Little-Parks Oscillation of Superconducting Möbius Strip
• Superconductivity on a Möbius strip: numerical studies on order parameter and quasiparticles