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We present a first-principles study of the electronic, magnetic, andtransport properties of the topological insulator Bi$_{2}$Te$_{3}$ doped withMn atoms in substitutional (Mn$_{\rm Bi}$) and interstitial van der Waals gappositions (Mn$_{\rm i}$), which act as acceptors and donors, respectively. Theeffect of native Bi$_{\rm Te}$- and Te$_{\rm Bi}$-antisite defects and theirinfluence on calculated electronic transport properties is also investigated.We have studied four models representing typical cases, namely (i)Bi$_{2}$Te$_{3}$ with and without native defects, (ii) Mn$_{\rm Bi}$ defectswith and without native defects, (iii) the same but for Mn$_{\rm i}$ defects,and (iv) the combined presence of Mn$_{\rm Bi}$ and Mn$_{\rm i}$. It was foundthat lattice relaxations around Mn$_{\rm Bi}$ defects play an important rolefor both magnetic and transport properties. The resistivity is stronglyinfluenced by the amount of carriers, their type, and by the relative positionsof the Mn-impurity energy levels and the Fermi energy. Our results indicatestrategies to tune bulk resistivities, and also help to uncover the location ofMn atoms in measured samples. Calculations indicate that at least two of theconsidered defects have to be present simultaneously in order to explain theexperimental observations, and the role of interstitials may be more importantthan expected.

Electronic and transport properties of the Mn-doped topological insulator Bi$_{2}$Te$_{3}$: A first-principles study