Detailed Measurements of the Quantized Flux States of Hollow Superconducting Cylinders

We have measured the magnetic flux trapped in superconducting tin cylinders (56-μm i.d., 0.7- to 5-μm walls, 24 mm long) and find that for most values of applied magnetic field the entire cylinder is in the same quantized flux state trapping an integral multiple of $\frac{\mathrm{hc}}{2e}\pm 1$%. For some applied fields we have evidence that the cylinder exists in a mixed state with bands along the length in states differing by one flux quantum.