Excitonic Aharonov-Bohm effect in a two-dimensional quantum ring

We study theoretically the optical properties of an exciton in a two-dimensional ring threaded by a magnetic flux. We model the quantum ring by a confining potential that can be continuously tuned from strictly one-dimensional to truly two-dimensional with finite radius-to-width ratio. We present an analytic solution of the problem when the electron-hole interaction is short ranged. The oscillatory dependence of the oscillator strength as a function of the magnetic flux is attributed to the Aharonov-Bohm effect. The amplitude of the oscillations changes upon increasing the width of the quantum ring. We find that the Aharonov-Bohm oscillations of the ground state of the exciton decrease with increasing the width, but, remarkably, the amplitude remains finite down to radius-to-width ratios less than unity. We attribute this resilience of the excitonic oscillations to the nonsimple connectedness of our chosen confinement potential with its centrifugal core at the origin.