  We present a first-principles study of the electronic, magnetic, and
transport properties of the topological insulator Bi$_{2}$Te$_{3}$ doped with
Mn atoms in substitutional (Mn$_{\rm Bi}$) and interstitial van der Waals gap
positions (Mn$_{\rm i}$), which act as acceptors and donors, respectively. The
effect of native Bi$_{\rm Te}$- and Te$_{\rm Bi}$-antisite defects and their
influence 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$_{\rm Bi}$ defects
with 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 found
that lattice relaxations around Mn$_{\rm Bi}$ defects play an important role
for both magnetic and transport properties. The resistivity is strongly
influenced by the amount of carriers, their type, and by the relative positions
of the Mn-impurity energy levels and the Fermi energy. Our results indicate
strategies to tune bulk resistivities, and also help to uncover the location of
Mn atoms in measured samples. Calculations indicate that at least two of the
considered defects have to be present simultaneously in order to explain the
experimental observations, and the role of interstitials may be more important
than expected.
