Analytic Aharonov-Bohm rings: Currents readout from Zeeman spectrum

This paper reports the work on the development and analysis of a model for quantum rings in which persistent currents are induced by Aharonov Bohm (AB) or other similar effects. The model is based on a centric and annual potential profile. The time-independent Schriidinger equation including an external magnetic field and an AB flux is analytically solved. The outputs, namely energy dispersion and wavefunctions, are analyzed in detail. It is shown that the rotation quantum number m is limited to small numbers, especially in weak confinement, and a conceptual proposal is put forward for acquiring the flux and eventually estimating the persistent currents in a Zeeman spectroscopy. The wavefunctions and electron distributions are numerically studied and compared to one-dimensional (1D) quantum well. It is predicated that the model and its solutions, eigen energy structure and analytic wavefunctions, would be a powerful tool for studying various electric and optical properties of quantum rings.