Theory of optical properties of II-VI semiconductor quantum dots containing a single magnetic ion in a strong magnetic field

Abstract

We present a microscopic theory of the magnetic field dependence of the optical properties of II--VI semiconductor quantum dots containing a single magnetic (Mn) impurity. The single-particle electron and heavy-hole states are described exactly by two-dimensional harmonic oscillators in a magnetic field, the Mn ion is treated as a spin of an isoelectronic impurity, and the quantum dot anisotropy is included perturbatively. The electron-hole direct, short-, and long-range exchange electron-hole Coulomb interactions, as well as the short-range spin-spin contact exchange interaction of the electron and the hole with the magnetic impurity is included. The electron-hole-Mn states are expanded in a finite number of configurations controlled by the number of confined electronic quantum dot shells and the full interacting Hamiltonian is diagonalized numerically in this basis. The absorption and emission spectrum is predicted as a function of photon energy, magnetic field, number of confined shells, and anisotropy. It is shown that the magnetic-field-induced enhancement of the exchange interaction of the Mn spin with the exciton is largely canceled by increased electron-hole Coulomb interactions. The predicted weak magnetic field dependence of the spacing of emission lines agrees well with the results of the spin model at low magnetic fields but differs at higher magnetic fields. Correlations in the exciton-Mn complex are predicted to determine absorption spectra.