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We investigate the properties of a single substitutional Mn impurity and itsassociated acceptor state on the (111) surface of Bi$_2$Se$_3$ topologicalinsulator. Combining ab initio calculations with microscopic tight-bindingmodeling, we identify the effects of inversion-symmetry andtime-reversal-symmetry breaking on the electronic states in the vicinity of theDirac point. In agreement with experiments, we find evidence that the Mn ion isin the ${+2}$-valence state and introduces an acceptor in the bulk band gap.The Mn-acceptor has predominantly $p$-character, and is localized mainly aroundthe Mn impurity and its nearest-neighbor Se atoms. Its electronic structure andspin-polarization are determined by the hybridization between the Mn $d$-levelsand the $p$-levels of surrounding Se atoms, which is strongly affected byelectronic correlations at the Mn site. The opening of the gap at the Diracpoint depends crucially on the quasi-resonant coupling and the strongreal-space overlap between the spin-chiral surface states and the mid-gapspin-polarized Mn-acceptor states.

Interplay between Mn-acceptor state and Dirac surface states in Mn-doped Bi$_2$Se$_3$ topological insulator