Trapping $\frac{h}{2e}$ Flux in Metals

We report on a new flux quantization phenomenon in metals. We study the response of normal metals to the presence of localized magnetic flux. We find that, due to backreaction effects, the metal traps 0 flux or $\frac{h}{2e}$ flux (half flux). We exhibit this effect both for metals pierced by magnetic solenoids and metals wrapping a magnetic solenoid. In the latter case we demonstrate the trapping of magnetic flux analytically. Furthermore, we find that as the solenoid is adiabatically turned off, a logarithmically enhanced localized equilibrium current persists, reflecting perfect defect-diamagnetism of the Fermi gas.