Landau quantization and the Aharonov-Bohm effect in a two-dimensional ring

Abstract

We propose an exactly soluble model for a ring with finite width. Exact energy spectra and wave functions are obtained analytically for a ring in the presence of both a uniform perpendicular magnetic field and a thin magnetic flux through the ring center. We use the model to study the Aharonov-Bohm (AB) effect in an ideal annular ring that is weakly coupled to both the emitter and the collector. It is found that, for such a weakly coupled ring in a uniform magnetic field, not only do the electron states in different subbands of the ring produce different AB frequencies, the clockwise and anticlockwise moving states in the same subband also lead to two different AB frequencies. Therefore, when many subbands in the ring are populated, the large number of different AB frequencies generally result in an aperiodic AB oscillation. More striking is that, even when only one subband is populated, the two AB frequencies corresponding to the states moving in opposite directions also cause beating in the AB oscillations. We have obtained explicit expressions for all these AB frequencies. Our results produce a clear explanation for the recent experimental observation of Liu and co-workers. \textcopyright{} 1996 The American Physical Society.