Aharonov-Bohm effect of excitons in nanorings

The magnetic field effects on excitons in an InAs nanoring are studied theoretically. By numerically diagonalizing the effective-mass Hamiltonian of the problem that can be separated into terms in center-of-mass and relative coordinates, we calculate the low-lying excitonic energy levels and oscillator strengths as a function of the ring width and the strength of an external magnetic field. It is shown that in the presence of Coulomb correlation, the so-called Aharonov-Bohm effect of excitons exists in a finite (but small) width nanoring. However, when the ring width becomes large, the non-simply-connected geometry of nanorings is destroyed, causing the suppression of the Aharonov-Bohm effect. The analytical results are obtained for a narrow-width nanoring in which the radial motion is the fastest one and adiabatically decoupled from the azimuthal motions. The conditional probability distribution calculated for the low-lying excitonic states allows identification of the presence of the Aharonov-Bohm effect. The linear optical susceptibility is also calculated as a function of the magnetic field, to be compared with the future measurements of optical emission experiments on InAs nanorings.