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Magnetic forces and localized resonances in electron transfer through quantum rings

We study the current flow through semiconductor quantum rings. In high magnetic field the current is usually injected to the arm of the ring preferred by classical magnetic forces. However, for narrow magnetic field intervals that appear periodically on the magnetic field scale the current is injected to the other arm of the ring. We indicate that the appearance of the anomalous -- non-classical -- current circulation results from Fano interference involving localized resonant states. The identification of the Fano interference is based on the comparison of the solution of the scattering problem with the results of the stabilization method. The latter employs the bound-state type calculations and allows to extract both the energy of metastable states localized within the ring and the width of resonances by analysis of the energy spectrum of a finite size system in function of its length. The Fano resonances involving states of anomalous current circulation become extremely narrow on both magnetic field and energy scales. This is consistent with the orientation of the Lorentz force that tends to keep the electron within the ring and thus increases the lifetime of the electron localization within the ring. Absence of periodic Fano resonances in electron transfer probability through a quantum ring containing an elastic scatterer is also explained.