One-dimensional ring with Kronig–Penney periodic potential: Persistent currents at full filling

We study the persistent electron current in a one-dimensional conducting GaAs ring with the Kronig–Penney periodic potential applied along the ring circumference (L). The periodic potential disturbs the free electron motion and changes the parabolic energy dispersion to a series of cosine-like energy bands separated by gaps. However, these cosine-like bands differ from the perfect cosine-shaped bands encountered in the lattice model with nearest-neighbor hopping or in the tight-binding model. Owing to this difference, in our model a non-zero persistent current exists when the energy band is completely filled by electrons. This current decays with increasing L exponentially, but we see measurable values for the properly chosen sample parameters. In contrast, in the tight-binding model the persistent current at full filling is zero which is a known result.