Magnetic quantum dots and rings in two dimensions

Abstract

We consider the motion of electrons confined to a two-dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is slowly decaying, bound states in magnetic quantum dots are indeed possible. Several example cases of such magnetic quantum dots are considered in which one can find the eigenvalues and eigenfunctions in closed form, including two hitherto unknown quasi-exactly-solvable models treated with confluent and biconfluent Heun polynomials. It is shown how a modulation of the strength of the magnetic field can exclude magnetic vortexlike states, rotating with a certain angular momenta and possessing a definite spin orientation, from forming. This indicates one may induce localization-delocalization transitions and suggests a mechanism for spin separation.