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 \ensuremath{\varphi}. We have calculated I as a function of flux \ensuremath{\varphi}, ring circumference L, temperature T, chemical potential \ensuremath{\mu}, and randomness W. We find that I decreases exponentially with T, that I decreases as ${W}^{2}$ for weak W and as exp(-L/\ensuremath{\xi}) for strong W, where \ensuremath{\xi} denotes the localization length, and that I is periodic in \ensuremath{\varphi} with period ${\ensuremath{\varphi}}_{0}$=hc/e. For certain averaging procedures the periodicity may change to ${\ensuremath{\varphi}}_{0}$/2.