  We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D
attractive fermionic Hubbard model. We extend previous results obtained for a
1D ring in which only azimuthal motion is considered, to a more general case of
2D annular lattices. In general, we show that the existence of the localization
effect, increased by the nonlinearity, makes the phenomenon in the 2D system
similar to the 1D case. However, the introduction of radial motion introduces
extra frequencies, different from the original isolated frequency corresponding
to the excitonic Aharonov-Bohm oscillations. If the circumference of the system
becomes large enough, the Aharonov-Bohm effect is suppressed.
