Quantum origin of half-flux oscillations in the magnetoresistance of metal cylinders

We use a tight-binding model of a metallic cylinder with a magnetic flux to show that, within Landauer’s formalism, the conductance has an oscillatory dependence on flux Φ with a period of ${\Phi }_0$/2=h/2e. The condition for this is that the disorder must be weak enough so that the localization length stays greater than the perimeter of the cylinder. Since the calculation does not employ ensemble averages nor any kind of inelastic process on the sample, we conclude that the half-flux period has purely quantum origin. We interpret it as a spectral effect due to an enhancement of quantum diffusion when Φ=(n+(1/2)${\Phi }_0$/2. At these fluxes the spectral degeneration of zero field is completely broken and this favors the resonant tunneling.