Valence band mixing versus higher harmonic generation in electric-dipole spin resonance

We study resonant transitions between hole states in a cylindrical quantum dot driven by an electric field. We find that the transitions obey selection rules for parities of the components of the Luttinger spinors of the initial and final states involved in the resonant transitions. We show, however, that additional resonances may appear in the spectrum as a result of breaking the transition rules when the initial or final states are close in energy to an another state. We study dots of varied radius-to-length ratios. For the quantum dots of disk-like geometry, the confinement leads to separation of the valence bands, and by proper tuning of the external magnetic field, the transitions between heavy-and light-hole bands can be observed. The increased length of the dot leads to mixing of the valence bands and at the same time results in an appearance of fractional resonances due to strong perturbation of the hole wavefunction by the oscillating field.