Electronic structure of Mn-doped III-V semiconductor quantum dots

Abstract

The electronic structure of GaAs and InAs quantum dots (QDs) containing a single substitutional Mn impurity is investigated in the envelope-function formalism. The Mn impurity in these compounds is known to be a shallow acceptor in the configuration ${d}^{5}+h$ and characterized by a strong antiferromagnetic $sp\text{\ensuremath{-}}d$ exchange interaction between the hole $(h)$ and the Mn ion. Our model for the hole states is based on the Luttinger Hamiltonian and the Coulomb potential with a central-cell correction that accounts for the observed binding energy and the effective $g$ factor in the bulk. The binding energy as well as the exchange contribution is found to increase with decreasing QD size. However, in contrast with the case of spherical nanocrystals (NCs), the binding energy in lens-shaped self-assembled QDs in the low-confinement limit is lower than that in the bulk because of their highly anisotropic shape. With an on-center impurity, NCs retain the bulk ${T}_{d}$ symmetry and the ground state is a $j=3/2$-like ${\ensuremath{\Gamma}}_{8}({T}_{d})$ level. In self-assembled QDs it splits into two doublets: ${\ensuremath{\Gamma}}_{6}$ $(|{j}_{z}|=1/2)$ and ${\ensuremath{\Gamma}}_{7}$ $(|{j}_{z}|=3/2)$ of ${D}_{2d}$, which mix in the presence of in-plane asymmetry, both belonging to ${\ensuremath{\Gamma}}_{5}$ of the reduced symmetry ${C}_{2v}$. The order and the splitting between the doublets depend on the degree of confinement and the strain-induced separation between the light- and heavy-hole valence bands. In lattice-matched GaAs/(Ga,Al)As QDs the ground-state doublet is $|{j}_{z}|=3/2$-like in the low-confinement limit. As the lateral size decreases there is a rapid crossover to a $|{j}_{z}|=1/2$-like ground state in QDs of typical sizes. On the other hand, in strained InAs/GaAs QDs the ground state is always $|{j}_{z}|=3/2$-like and the splitting relatively large. The $sp\text{\ensuremath{-}}d$ coupling with the Mn spin $S=5/2$ finally leads to a splitting of the ground-state doublet into six doubly-degenerate levels. The components are close to one another as the effective exchange parameters are an order of magnitude smaller than in the bulk. Our results thoroughly contradict the previously adopted picture based on treating the confinement potential as a small perturbation to the bulk impurity levels. We also consider the lowest two-hole states: the ground state in InAs/GaAs QDs is a singlet almost uncoupled to the Mn spin. We deduce the zero-field fine structure of the excitonic transitions and compare the results with the recently reported photoluminescence spectra.