Energy structure of quantum rings in a magnetic field

Electron and hole energy levels of self-assembled quantum rings [A. Lorke et al., Phys. Rev. Lett. 84, 4537 (2000)] in a magnetic field are calculated. We go beyond the simple two-dimensional ring model with parabolic confining potential and use the k·p method with rectangular band-offset potentials in three dimensions. The one-band model is employed for the electron states and the two-band Hamiltonian is used for the hole states. Our calculations describe qualitatively well the positions of experimental resonances found in the far-infrared transmission spectra. The calculated hole energy spectrum differs significantly from the electron one. This difference originates from the light-hole and heavy-hole intersubband mixing.