Electrical manipulation of Rashba spin-orbit coupling in the two-dimensional transition metal dichalcogenide
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摘要: 本文采用基于密度泛函理论的第一性原理计算方法，对6种二维过渡金属硫化物MX2（M=Mo，W；X=S，Se，Te）中的Rashba自旋轨道耦合效应进行了系统研究.对6种MX2材料施加垂直方向电场，发现阴离子X对于电场诱导的Rashba自旋轨道耦合效应起主要作用：X原子序数越大，电场诱导的Rashba劈裂也越大；阳离子M被阴离子X覆盖，对电场诱导的Rashba自旋劈裂影响较弱.因此，6种MX2单层的Rashba自旋劈裂大小依次为：WTe2 > MoTe2 > WSe2 > MoSe2 > WS2 > MoS2.施加电场后，从布里渊区中心Γ点到布里渊区边界K/K'点，自旋方向二维平面内转向垂直方向，并且随着电场的增加，面内自旋成分逐渐增加.
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关键词:
- 二维过渡金属硫化物 /
- Rashba自旋轨道耦合 /
- 第一性原理计算
Abstract: Using the first-principles density functional theory calculations, we investigate the Rashba spin-orbit coupling of the transition metal dichalcogenide (TMD) monolayers MX2(M=Mo, W; X=S, Se, Te) induced by the external electric field. It is found that the anions X play an important role on the Rashba spin-orbit coupling effect. With the increase of the atomic number of X, Rashba spin-orbit splitting around the Γ point increases more distinctively, and the external electric field can hardly influence the cations because of the coverage by the anions. Thus the strength of the Rashba spin-orbit coupling follows the sequence:WTe2 > MoTe2 > WSe2 > MoSe2 > WS2 > MoS2. Furthermore, the distribution of the spin polarization along the high symmetry line Γ-K/K' turns from the vertical direction to the two-dimensional plane under the external electric fields, and the in-plane spin polarization distribution rises with the increase of the external electric field. -
图 1 (a)、(b)二维$MX_{2}$结构的侧视图和俯视图, 其中蓝色球表示过渡金属元素$M$(Mo, W), 橙色球表示硫族元素$X$(S, Se, Te); (c)二维$MX_{2}$的第一布里渊区示意图, 其中$\overrightarrow{b} _1 $和$\overrightarrow{b} _2 $为倒格子基矢; (d)自旋简并的能带示意图; (e) Rashba自旋劈裂能带示意图
Fig. 1 (a) Side view and (b) top view of the $MX_{2}$ monolayer structure, with the blue and the orange ball representing transition metals and chalcogenides, respectively; (c) The first Brillouin zone of the $MX_{2}$ monolayer with the reciprocal lattice vector $\overrightarrow{b} _1 $ and $\overrightarrow{b} _2 $; Schematic band structure for (d) spin degeneracy and (e) Rashba splitting
图 3 (a)-(c)外加电场$E_\text{ext}$=0 V/Å, 0.1 V/Å, 0.8 V/Å时, 单层WTe$_{2}$价带顶能带中的自旋分布图
Fig. 3 (a)-(c) Distribution of the spin polarization of the WTe$_{2}$ monolayer in the highest valence band under the external electric fields $E_\text{ext}$=0 V/Å, 0.1 V/Å, 0.8 V/Å, respectively
图 4 (a)-(c)单层WS$_{2}$、WSe$_{2}$、WTe$_{2}$分别在外加电场$E_\text{ext}$=0 V/Å, 0.2V/Å, 0.4 V/Å, 0.8 V/Å时, $\varGamma $点附近能带结构图
Fig. 4 (a)-(c) Band structure of the WS$_{2}$, WSe$_{2}$ and WTe$_{2}$ monolayers under the external electric fields $E_\text{ext}$=0 V/Å, 0.2V/Å, 0.4 V/Å, 0.8 V/Å, respectively
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