Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film

We study the possibility of realizing quantum anomalous Hall (QAH) effect with tunable Chern number through doping magnetic elements in a multilayer topological insulator film. We find that high Chern number QAH phases exist in ideal neutral samples and can make transition to another QAH phase directly by means of tuning exchange field strength or sample thickness. With the help of an extended Haldane model, we demonstrate the physical mechanism of the tunable Chern number QAH phase. We show that the high Chern number QAH phases are robust against weak magnetic and nonmagnetic disorders.