Hong Jisook, Rhim Jun-Won, Kim Changyoung, Ryong Park Seung, Hoon Shim Ji
Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea.
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Sci Rep. 2015 Sep 1;5:13488. doi: 10.1038/srep13488.
We report on quantitative comparison between the electric dipole energy and the Rashba band splitting in model systems of Bi and Sb triangular monolayers under a perpendicular electric field. We used both first-principles and tight binding calculations on p-orbitals with spin-orbit coupling. First-principles calculation shows Rashba band splitting in both systems. It also shows asymmetric charge distributions in the Rashba split bands which are induced by the orbital angular momentum. We calculated the electric dipole energies from coupling of the asymmetric charge distribution and external electric field, and compared it to the Rashba splitting. Remarkably, the total split energy is found to come mostly from the difference in the electric dipole energy for both Bi and Sb systems. A perturbative approach for long wave length limit starting from tight binding calculation also supports that the Rashba band splitting originates mostly from the electric dipole energy difference in the strong atomic spin-orbit coupling regime.
我们报告了在垂直电场下铋（Bi）和锑（Sb）三角单层模型系统中电偶极子能量与 Rashba 能带分裂之间的定量比较。我们对具有自旋轨道耦合的 p 轨道同时进行了第一性原理计算和紧束缚计算。第一性原理计算表明两个系统中均存在 Rashba 能带分裂。它还显示了由轨道角动量引起的 Rashba 分裂能带中的不对称电荷分布。我们通过不对称电荷分布与外部电场的耦合计算了电偶极子能量，并将其与 Rashba 分裂进行了比较。值得注意的是，发现总分裂能量主要来自 Bi 和 Sb 系统电偶极子能量的差异。从紧束缚计算出发的长波长极限微扰方法也支持，在强原子自旋轨道耦合 regime 中，Rashba 能带分裂主要源于电偶极子能量差。
