Half-Flux-Quantum Magnetoresistance Oscillations in Disordered Metal Rings

The behavior of the magnetoresistance of single and arrays of disordered metal rings is investigated. The average localization length, $L_c$, which is related to the conductance, is found to oscillate with a strong half-flux-quantum harmonic at low magnetic field. The ratio of the amplitude of the full-flux oscillations versus the half-flux oscillations is shown to decrease with the number of rings. All numerical results follow a universal law where the amplitude of oscillations of $L_c$ is found to be proportional to the square of the ratio of $L_c$ to the perimeter of the ring. At high magnetic fields, full-flux oscillations are observed.