Is the Magnetic Field Necessary for the Aharonov-Bohm Effect in Mesoscopics?

We predict a new class of topological mesoscopic phenomena in absence of external magnetic field, based on combined action of the nonequilibrium nuclear spin population and charge carrier spin-orbit interaction. We show that Aharonov-Bohm-like oscillations of the persistent current in $\mathrm{GaAs}/\mathrm{AlGaAs}$ based mesoscopic rings may exist in the absence of the external magnetic field, provided that a topologically nontrivial strongly nonequilibrium nuclear spin population is created. This phenomenon is due to the breaking, via the spin-orbit coupling, of the clockwise-anticlockwise symmetry of the charge carriers momentum, which results in an oscillatory in time persistent current.