Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping

In this work, we investigate the topological phase transitions in an effective model for a topological thin film with high-frequency pumping. In particular, our results show that the circularly polarized light can break the time-reversal symmetry and induce the quantum anomalous Hall insulator (QAHI) phase. Meanwhile, the bulk magnetic moment can also break the time-reversal symmetry. Therefore, it shows rich phase diagram by tunning the intensity of the light and the thickness of the thin film. Using the parameters fitted by experimental data, we give the topological phase diagram of the Cr-doped Bi$_{2}$Se$_{3}$ thin film, showing that by modulating the strength of the polarized optical field in an experimentally accessible range, there are four different phases: the normal insulator phase, the time-reversal-symmetry-broken quantum spin Hall insulator phase, and two different QAHI phases with opposite Chern numbers. Comparing with the non-doped Bi$_{2}$Se$_{3}$, it is found that the interplay between the light and bulk magnetic moment separates the two different QAHI phases with opposite Chern numbers. The results show that an intrinsic magnetic topological insulator with high-frequency pumping is an ideal platform for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.