Magneto-optical properties of nanocrystals:  Zeeman splitting

We discuss different aspects of the Zeeman splitting in optical properties of II-VI spherical quantum dots in presence of a external magnetic field B. A systematic study of the energy eigenvalues, wave functions, and their dominant symmetries within the $8\times 8$ $\mathbf{k}\cdot \mathbf{p}$ Kane-Weiler formalism, allowing the inclusion of the conduction- valence-band coupling, nonparabolicity, and mixing of the electronic and spin states, is presented. The analysis of symmetries inherent in the $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian leads to sets of basis functions that can be separated into two independent Hilbert subspaces. The linear and quadratic Zeeman splitting in the quantum dot have been studied in the strong confinement regime. A detailed discussion of the symmetries associated with the electronic levels and the magneto-optical selection rules for interband transitions are derived. We also calculated the optical oscillator strengths and their corresponding magnetoabsorption coefficient for Faraday and Voigt configurations. It shows that the effective Landé g factor, obtained theoretically, and diamagnetic shift can be tested experimentally by complementary optical spectra measured in Faraday and Voigt geometries.