Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

We report on the electronic properties of few interacting electrons confined in a parabolic quantum dot based on a theoretical approach developed to investigate the influence of Bychkov-Rashba spin-orbit (SO) interaction on such a system. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Here we present accurate results for the energy levels and optical-absorption spectra for parabolic quantum dots containing up to four interacting electrons, in the presence of spin-orbit coupling and under the influence of an externally applied, perpendicular magnetic field. We have described in detail a very accurate numerical scheme to evaluate these quantities. We have evaluated the effects of the SO coupling on the Fock-Darwin spectra for quantum dots made out of three different semiconductor systems, InAs, InSb, and GaAs. The influence of SO coupling on the single-electron spectra manifests itself by primarily lifting the degeneracy at zero magnetic field, rearrangement of some of the energy levels at small magnetic fields, and level repulsions at high fields. These results are explained as due to mixing of different spinor states for increasing strength of the SO coupling. As a consequence, the corresponding absorption spectra reveal anticrossing structures in the two main lines of the spectra. For interacting many-electron systems we observed the appearence of discontinuities, anticrossings, and new modes that appear in conjunction with the two main absorption lines. These additional features arise entirely due to the SO coupling and are a consequence of level crossings and level repulsions in the energy spectra. An intricate interplay between the SO coupling and the Zeeman energies is shown to be responsible for these additional features seen in the energy spectra. Optical absorption spectra for all three types of quantum dots studied here show a common feature: new modes appear, mostly near the upper main branch of the spectra around 2 T, that become stronger with increasing SO coupling strength. Among the three types of systems considered here, the optical signature of the SO interaction is found to be the strongest in the absorption spectra of the GaAs quantum dot, but only at very large values of the SO coupling strength, and appears to be the weakest for the InSb quantum dot. Experimental observation of these modes that appear solely due to the presence of the SO coupling would provide a rare glimpse into the role of the SO coupling in nanostructured quantum systems.