First-principles study of magnetic ion doping in thin film Bi$_2$Se$_3$: electronic structure and topological phase

We study the quantum anomalous Hall state in magnetic ion-doped Bi$_2$Se$_3$ thin films. By using first-principles density functional theory, we investigate this electronic structure and identify its topological phase. We find that magnetic ion doping induces the exchange field splitting and changes the spin-orbit coupling strength. As the doping concentration increases, the exchange field splitting strength increases and the spin-orbit coupling strength may decrease depending on the type of magnetic ion. Based on these results, we show that the quantum anomalous Hall state in the doped Bi$_2$Se$_3$ thin film emerges at a certain range of doping concentration. The Hall conductance of the doped Bi$_2$Se$_3$ thin film will also be discussed with various doping concentrations.