The magnetic flux frozen in a loop/hole (plus its -layer) will always be quantized. However, the value of the flux quantum is equal to only when the path/trajectory around the hole described above can be chosen so that it lays in the superconducting region without screening currents, i.e. several away from the surface. There are geometries where this condition cannot be satisfied, e.g. a loop made of very thin () superconducting wire or the cylinder with the similar wall thickness. In the latter case, the flux has a quantum different from .