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Band-structure topologies of graphene: Spin-orbit coupling effects from first principles

机译:石墨烯的能带结构拓扑:第一原理的自旋轨道耦合效应

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摘要

The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap of 24 μeV (0.28 K) at the K(K') point. It is shown that the previously accepted value of 1 μeV, coming from the σ-π mixing, is incorrect due to the neglect of d and higher orbitals whose contribution is dominant due to symmetry reasons. The transverse electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of 10 μeV (0.11 K) per Vm, coming from the σ-π mixing. A "miniripple" configuration with every other atom shifted out of the sheet by less than 1 % differs little from the intrinsic case.
机译:使用线性化增强平面波方法,从第一原理出发研究了存在自旋轨道耦合和横向电场的情况下石墨烯的电子能带结构。自旋轨道耦合在K(K')点处打开一个24μeV(0.28 K)的间隙。结果表明,由于σ和π的混合,先前接受的1μeV值是不正确的,这是由于忽略了d和更高的轨道,而由于对称性原因,它们的贡献占主导地位。横向电场会引起来自σ-π混合的10 VeV(0.11 K)/ V / nm的附加(外部)Bychkov-Rashba型分裂。每隔一个原子从薄片中移出小于1%的“微波纹”构型与本征情况几乎没有什么不同。

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