Persistent currents of noninteracting electrons in one-, two-, and three-dimensional thin rings

We thoroughly study the persistent current of noninteracting electrons in one-, two-, and three-dimensional thin rings. We find that the results for noninteracting electrons are more relevant for individual mesoscopic rings than hitherto appreciated. The current is averaged over all configurations of the disorder, whose amount is varied from zero up to the diffusive limit, keeping the product of the Fermi wave number and the ring's circumference constant. Results are given as functions of disorder and aspect ratios of the ring. The magnitude of the disorder-averaged current may be larger than the root-mean-square fluctuations of the current from sample to sample even when the mean-free path is smaller, but not too small, than the circumference of the ring. Then a measurement of the persistent current of a typical sample will be dominated by the magnitude of the disorder-averaged current.