Sliding- and twist-tunable valley polarization in bilayerNiI2

Valley, as an emerging degree of freedom of electron, has attracted extensive attention on account of its huge potential in electronic component technology. Two-dimensional (2D) materials provide an ideal platform for the research of valleytronics. Here, we study the sliding and twist effects on valley of bilayer NiI2 by the first-principles calculations. For a monolayer, spatial inversion symmetry maintains the degeneracy of two valleys. In the AA stacking bilayer, which can be obtained by a vertical translation operation on a monolayer structure, the valley band splitting is absent due to the ˆ𝑃⁢ˆ𝑇 joint symmetry. The interlayer sliding of the AA stacking bilayer can not break ˆ𝑃⁢ˆ𝑇 joint symmetry and therefore there is not valley band splitting in a sliding system with respect to AA stacking. For the AA′ stacking bilayer, the valley band splitting occurs while the valley polarization is still absent as the ˆ𝑀𝑍⁢ˆ𝑇 joint symmetry. Different from the AA stacking system, ˆ𝑀𝑍⁢ˆ𝑇 joint symmetry of the AA′ system can be broken by interlayer sliding, and the valley polarization is realized. Furthermore, valley polarization is studied and it existed in twisted moiré structures with twist angles of 13.174∘, 21.787∘, 27.796∘, 32.204∘, 38.213∘, and 46.826∘, as the twisting breaks the spatial inversion symmetry. Our results broaden the valley polarization materials by interlayer sliding and twisting of 2D bilayer structures.