Magnetic flux quantum
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TODO is there any relationship between this and the Josephson effect?
Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.
This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.
Video "Superconducting Qubit by NTT SCL (2015)" suggests that anything in between gets cancelled out by a superposition of current in both directions.