Fluxoid Quantization in a Multiply-Connected Superconductor

Abstract

The transition temperatures of thin-walled superconducting hollow cylinders of very small diameters (approximately $1\mu$) were measured as a function of the applied magnetic field in the axial direction. Oscillations with a period of $\frac{\mathrm{hc}}{2e}$ in the magnetic flux through the cylinder were observed in the transition temperature $T_c$. This is a consequence of "fluxoid" quantization which was originally predicted by Fritz London. The basic unit of magnetic flux $\frac{\mathrm{hc}}{2e}$ is explained in terms of London's original arguments and the result from the BCS theory that the charge carriers in a superconductor are pairs of electrons. Measurements were made on Sn, In, Pb, Al, and Sn-In alloys. A periodicity in the magnetic flux of $\frac{\mathrm{hc}}{2e}$ was observed in all of the samples. The amplitude of $\Delta T_c$ varied from approximately ${10}^{-5\mathrm{}}$ to ${10}^{-3\mathrm{}}$°K and depended upon the temperature, the radius, and the mean free path of the cylindrical sample.