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.

中文翻译：

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双层 NiI2 中的滑动和扭曲可调谷极化


谷作为一种新兴的电子自由度，因其在电子元件技术方面的巨大潜力而受到广泛关注。二维 （2D） 材料为 valleytronics 的研究提供了理想的平台。在这里，我们通过第一性原理计算研究了双层 NiI2 谷的滑动和扭曲效应。对于单层，空间反转对称性保持了两个谷的简并性。在可以通过对单层结构进行垂直平移操作获得的 AA 堆叠双层中，由于 ˆPˆT 接头对称性，不存在谷带分裂。AA 堆叠双层的层间滑动不会打破 ˆPˆT 接头对称性，因此相对于 AA 堆叠，滑动系统中不存在谷带分裂。对于 AA′ 堆叠双层，当 ˆMZˆT 接头对称性仍然不存在谷极化时，会发生谷带分裂。与 AA 堆叠系统不同，AA' 系统的 ˆMZˆT 接头对称性可以通过层间滑动来打破，实现谷极化。此外，研究了谷极化，它存在于扭曲的莫尔结构中，扭曲角分别为 13.174∘、21.787∘、27.796∘、32.204∘、38.213∘ 和 46.826∘，因为扭曲打破了空间反转对称性。我们的结果通过二维双层结构的层间滑动和扭曲拓宽了谷极化材料。