behaves under the influence of the vector potential A in the same way as the phase of a single electron. Therefore the BCS condensate flowing around a closed path in a multiply connected superconducting sample acquires a phase difference Δφ determined by the magnetic flux ΦB through the area enclosed by the path (via Stokes' theorem and ), and given by: This phase effect is responsible for the quantized-flux requirement and the Little–Parks effect in superconducting loops and empty cylinders. The quantization occurs because the superconducting wave function must be single valued in a loop or an empty superconducting cylinder: its phase difference Δφ around a closed loop must be an integer multiple of 2π, with the charge for the BCS electronic superconducting pairs. If the period of the Little–Parks oscillations is 2π with respect to the superconducting phase variable, from the formula above it follows that the period with respect to the magnetic flux is the same as the magnetic flux quantum, namely Applications Little–Parks oscillations are a widely used proof mechanism of Cooper pairing. One of the good example is the study of the Superconductor Insulator Transition. The challenge here is to separate Little–Parks oscillations from weak (anti-)localization, as in Altshuler et al. results, where authors observed the Aharonov–Bohm effect in a dirty metallic films. History Fritz London predicted that the fluxoid is quantized in a multiply connected superconductor. Experimentally has been shown, that the trapped magnetic flux existed only in discrete quantum units h/2e. Deaver and Fairbank were able to achieve the accuracy 20–30% because of the wall thickness of the cylinder. Little and Parks examined a "thin-walled" (Materials: Al, In, Pb, Sn and Sn–In alloys) cylinder (diameter was about 1 micron) at T very close to the transition temperature in an applied magnetic field in the axial direction. They found magnetoresistance oscillations with the period consistent with h/2e. What they actually measured was an infinitely small changes of resistance versus temperature for (different) constant magnetic field, as it shown in Fig. References Condensed matter physics Superconductivity