A Simple Formula for the Persistent Current in Disordered 1D Rings: Parity and Interaction Effects

The general expression for the persistent current of 1D noninteracting electrons in a disorder potential with smooth scattering data is derived for zero temperature. On the basis of this expression the parity effects are discussed. It is shown that the electron-electron interaction may give rise to an unusual size-dependence of the current amplitude due to renormalized backscattering from the disorder potential.