Band-structure topologies of graphene: Spin-orbit coupling effects from first principles
Band-structure topologies of graphene: Spin-orbit coupling effects from first principles
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DOI：
10.1103/physrevb.80.235431
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发表时间：
2009-12-01
影响因子：
3.7
通讯作者：
Fabian, J.
中科院分区：
文献类型：
--
作者：
Gmitra, M.;Konschuh, S.;Fabian, J.
利用线性化增广平面波方法，从第一性原理出发，研究了自旋-轨道耦合和横向电场作用下石墨烯的电子能带结构。自旋-轨道耦合在K(K-‘)点处打开了24微eV(0.28K)的间隙。结果表明，由于对称性的原因，忽略了贡献占主导地位的d轨道和更高轨道，使得以前所接受的来自sigma-pi混合的1µeV是不正确的。横向电场产生额外的(外在)Bychkov-Rashba型分裂，每V/nm约10微米eV(0.11K)，这是由sigma-pi混合引起的。每隔一个原子向外移动不到1%的“微涟漪”构型与本征情况几乎没有什么不同。
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 mu eV (0.28 K) at the K(K-') point. It is shown that the previously accepted value of 1 mu eV, coming from the sigma-pi 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 mu eV (0.11 K) per V/nm, coming from the sigma-pi mixing. A "miniripple" configuration with every other atom shifted out of the sheet by less than 1% differs little from the intrinsic case.