Possible way to achieve valley-polarized quantum anomalous Hall insulator

The valley-polarized quantum anomalous Hall insulator (VQAHI), which combines valleytronics and topology in one material, provides a path toward integrating valleytronics, topological quantum effects, and spintronics. Here, we propose a way of realizing VQAHIs in tetragonal quantum anomalous Hall insulators (QAHIs) by introducing valley polarization, which can be achieved by breaking C4 rotational symmetry. We use a concrete example of a QAHI Fe2I2 monolayer, where there are equivalent valleys along the Γ-X and Γ-Y lines in momentum space, to illustrate our proposal through first-principle calculations. By applying uniaxial strain along the x direction, the rotational symmetry C4 is reduced into C2, which induces valley polarization. With uniaxial strain from a compressive one to a tensile one, valley polarization transition can be induced. Moreover, the nonzero Berry curvature around valleys can produce the anomalous valley Hall effect. With the considered strain range, the quantum anomalous Hall properties can be maintained. Therefore, a VQAHI can be realized in strained Fe2I2. Our works propose an experimentally feasible way to realize valley polarization and VQAHIs.