  The Hall effect, the anomalous Hall effect and the spin Hall effect are
fundamental transport processes in solids arising from the Lorentz force and
the spin-orbit coupling respectively. The quantum versions of the Hall effect
and the spin Hall effect have been discovered in recent years. However, the
quantized anomalous Hall (QAH) effect has not yet been realized experimentally.
In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling
combine to give rise to a topologically non-trivial electronic structure,
leading to the quantized Hall effect without any external magnetic field. In
this work, based on state-of-art first principles calculations, we predict that
the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$
form magnetically ordered insulators when doped with transition metal elements
(Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor
where free carriers are necessary to mediate the magnetic coupling. Magnetic
order in two-dimensional thin films gives rise to a topological electronic
structure characterized by a finite Chern number, with quantized Hall
conductance $e^{2}/h$. Experimental realization of the long sought-after QAH
insulator state could enable robust dissipationless charge transport at room
temperature.
