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We investigate in-gap states emerging when a single $3d$ transition metalimpurity is embedded in topological insulators (Bi$_2$Te$_3$ and Bi$_2$Se$_3$).We use a combined approach relying on first-principles calculations and anAnderson impurity model. By computing the local density of states of Cr, Mn, Feand Co embedded not only in surfaces of Bi$_2$Te$_3$ and of Bi$_2$Se$_3$ butalso in their bulk phases, we demonstrate that in-gap states originate from thehybridization of the electronic states of the impurity with bulk bands and notwith the topological surface states as it is usually assumed. This finding isanalyzed using a simplified Anderson impurity model. These observations are incontradiction with the prevailing models used to investigate the magneticdoping of topological insulators [R. R. Biswas et al. PRB 81, 233405 (2010), A.M. Black-Schafer et al. PRB 91, 201411 (2015)], which attribute the origin ofthe in-gap states to the hybridization with the topological surface states.

Ab initio investigation of impurity-induced in-gap states in Bi$_2$Te$_3$ and Bi$_2$Se$_3$