  The optical exciton Aharonov-Bohm effect, i. e. an oscillatory component in
the energy of optically active (bright) states, is investigated in nanorings.
It is shown that a small effective electron mass, strong confinement of the
electron, and high barrier for the hole, achieved e. g. by an InAs nanoring
embedded in an AlGaSb quantum well, are favorable for observing the optical
exciton Aharonov-Bohm effect. The second derivative of the exciton energy with
respect to the magnetic field is utilized to extract Aharonov-Bohm oscillations
even for the lowest bright state unambiguously. A connection between the
theories for infinitesimal narrow and finite width rings is established.
Furthermore, the magnetization is compared to the persistent current, which
oscillates periodically with the magnetic field and confirms thus the
non-trivial (connected) topology of the wave function in the nanoring.
