Persistent currents in small one-dimensional metal rings

Abstract

We have performed analytical calculations and computer simulations to study the persistent current I in small isolated one-dimensional metal rings enclosing a magnetic flux φ. We have calculated I as a function of flux φ, ring circumference L, temperature T, chemical potential μ, and randomness W. We find that I decreases exponentially with T, that I decreases as $W^2$ for weak W and as exp(-L/ξ) for strong W, where ξ denotes the localization length, and that I is periodic in φ with period ${\phi }_0$=hc/e. For certain averaging procedures the periodicity may change to ${\phi }_0$/2.