The paper discusses the quantized anomalous Hall (QAH) effect in magnetic topological insulators, specifically focusing on the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$. These materials, when doped with transition metal elements (Cr or Fe), form magnetically ordered insulators without the need for free carriers to mediate magnetic coupling, unlike conventional dilute magnetic semiconductors. The authors predict that these doped compounds will exhibit a topologically non-trivial electronic structure characterized by a finite Chern number, leading to a quantized Hall conductance of $e^2/h$. This effect is achieved through the spontaneous magnetic moments and spin-orbit coupling, which combine to create a band inversion near the $\Gamma$ point. The paper also explores the Van-Vleck paramagnetism in these materials, which provides a mechanism for ferromagnetic ordering. Through mean field theory and first-principles calculations, the authors demonstrate that the Curie temperature for ferromagnetic ordering can be as high as 70K. Additionally, they show that the QAH effect can be realized in 2D thin films of these materials, with the Hall conductance quantizing to $e^2/h$ under certain conditions. This work highlights the potential for robust, dissipationless charge transport at room temperature in QAH insulators, opening new avenues for low-power electronic devices.The paper discusses the quantized anomalous Hall (QAH) effect in magnetic topological insulators, specifically focusing on the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$. These materials, when doped with transition metal elements (Cr or Fe), form magnetically ordered insulators without the need for free carriers to mediate magnetic coupling, unlike conventional dilute magnetic semiconductors. The authors predict that these doped compounds will exhibit a topologically non-trivial electronic structure characterized by a finite Chern number, leading to a quantized Hall conductance of $e^2/h$. This effect is achieved through the spontaneous magnetic moments and spin-orbit coupling, which combine to create a band inversion near the $\Gamma$ point. The paper also explores the Van-Vleck paramagnetism in these materials, which provides a mechanism for ferromagnetic ordering. Through mean field theory and first-principles calculations, the authors demonstrate that the Curie temperature for ferromagnetic ordering can be as high as 70K. Additionally, they show that the QAH effect can be realized in 2D thin films of these materials, with the Hall conductance quantizing to $e^2/h$ under certain conditions. This work highlights the potential for robust, dissipationless charge transport at room temperature in QAH insulators, opening new avenues for low-power electronic devices.