Using a relativistic symmetrized linear augmented cylindrical wave method, we investigated a formation of spin minigaps due to a torsion strain of the nonchiral hexagonal and gear-like armchair ( n, n) and zigzag ( n, 0) silicon nanotubes (SiNTs). In the absence of mechanical twisting, the hexagonal ( n, n) SiNTs have an inversion symmetry and metallic band structures with the spin-degenerate states at the Fermi region. The torsion deformation of hexagonal armchair SiNT breaks the inversion symmetry, transforming it into the chiral system with the right or left screw axis. Due to the combined effect of spin–orbit coupling and low-symmetry perturbation, the degeneration of levels is completely removed and the α and β type bands are formed. The torsion deformation works like a switch, the opposite twisting directions result in the opposite chirality of tubules and induce the opposite spin currents due to Rashba effect. Even in the ideal non-twisted gear-like SiNTs, there is no inversion symmetry. Such tubules have semiconductor band structures with the spin–orbit splittings of the valence and conduction bands. Twisting causes an increase in the antisymmetric component of the potential leading to a monotonic increase in the spin gaps.

中文翻译：

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用于手性自旋电子学的扭曲硅纳米管中的 Rashba 自旋轨道相互作用效应

使用相对论对称线性增强柱面波方法，我们研究了由于非手性六角形和齿轮状扶手椅 ( n, n) 和锯齿形 ( n, 0) 硅纳米管 (SiNT) 的扭转应变而形成的自旋微间隙。在没有机械扭曲的情况下，六方 ( n, n) SiNT 具有反转对称性和金属能带结构，在费米区具有自旋简并态。六边形扶手椅 SiNT 的扭转变形打破了反转对称性，将其转化为具有右旋轴或左旋轴的手征系统。由于自旋轨道耦合和低对称性微扰的共同作用，能级退化被完全消除，形成了 α 和 β 型能带。扭转变形就像一个开关，相反的扭曲方向导致小管的相反手性，并由于 Rashba 效应引起相反的自旋电流。即使在理想的非扭曲齿轮状 SiNT 中，也不存在反转对称性。这种细管具有半导体能带结构，具有价带和导带的自旋轨道分裂。扭曲导致势能的反对称分量增加，导致自旋间隙单调增加。