## Abstract 

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 insu- lators 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 charac- terized 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. 

