PERSISTENT CURRENTS AND EDGE STATES IN A MAGNETIC-FIELD

We investigate equilibrium electron currents in an ideal two-dimension al ring (of radii R1 < R 2 ). The most striking result emerges when th e conditions for the existence of edge and bulk states are met, namely R 2 - R1 much greater than a(H) where a(H) is the magnetic length. If the Fermi energy lies in a gap between two Landau levels, the current (as a function of electron density) displays violent fluctuations (in sign and in absolute value), which is quite unusual for systems witho ut disorder. The fluctuations in sign result from the alternative cont ributions of inner and outer occupied edge states below the Fermi ener gy, while those in absolute value originate from the apparent symmetry between the slopes of the energy curves near the two opposite edge st ates. On the other hand, when the Fermi energy is locked on a Landau l evel, the current has a plateau as a function of electron density. Its value at a plateau represents the contribution to the current of all the edge states in the lower Landau levels.