Magneto-optical transitions in nanoscopic rings

Near-infrared spectra of self-assembled quantum rings are calculated using the $\mathbf{k}\cdot \mathbf{p}$ method with rectangular band-offset potentials in three dimensions. The effective-mass model with energy-dependent mass is employed for the electron states and the four-band Hamiltonian for the hole states. Two different ways to include the magnetic-field interaction term in the four-band Hamiltonian are compared. Our calculations describe well, qualitatively, the absorption spectrum measured by Petterson et al. [H. Petterson, R. J. Warburton, A. Lorke, K. Karrai, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff, Physica E 6, 510 (2000)]. and the photoluminescence magnetoresonances recently achieved by Haft et al. [D. Haft, C. Schulhauser, A. O. Govorov, R. J. Warburton, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, Physica E 13, 165 (2002)]. The possibility of finding the “optical” Aharanov-Bohm effect in the state-of-the-art self-assembled InGaAs quantum rings is also discussed.