[论文解读] Geometrical structure and the electron transport properties of monolayer and bilayer silicene near the semimetal-insulator transition point in tight-binding model

Chen-Huan Wu|arXiv (Cornell University)|Apr 30, 2018

Graphene research and applications参考文献 40被引用 13

一句话总结

本研究利用包含自旋、谷和亚晶格自由度的多带近似紧束缚模型，研究了单层和双层硅烯在半导体-绝缘体相变点附近的电子输运及相变行为。结果表明，单层硅烯的临界Hubbard U为9 eV，AA堆叠的双层硅烯或掺杂杂质的单层硅烯为12 eV，且光学电导率和屏蔽效应在决定相变点附近的输运性质中起关键作用。

ABSTRACT

We investigate the electron properties of the monolayer and bilayer silicene which is the honeycomb lattice consist of silicon atoms, including the optical conductivity and charged impurity scattering, due to the quasipatricle Dirac-like behaviors near the K-point of silicene. The spin, valley, sublattice degrees of freedom are taken into consider in the multi-band tight-binding model. In momentum space, the scattering matrix which connects the two bare (without interaction) Green's functions in the quasiparticle momentum transport process, could be momentum-independent for the single impuirity configuration, which is similar to the case with small Coulomb coupling in the low-energy Dirac semimetallic system. While in the zero-frequency limit, or the frequency-independent case in the strong Coulomb coupling regime, the static polarization can be obtained by the random-phase-approximation, and it's important for the determination of the screened Coulomb scattering by the charge impurity. The antiferromagnetic order in the silicene is Hubbard-U-dependent, unlike the square lattice which with the antiferromagnetic ground state, and provides the premise of the phase transition from the nonmagnetic semimetal phase to the insulator one. We found that in the absence of electric field, the critical value of the phase transition from semimetal to insulator is 9 eV for the clear monolayer silicene, and is 12 eV for the 2nd AA-stacked bilayer silicene or the dirty monolayer silicene whcih with impurity strength 4 eV. While the behaviors of 1st AA-stacked bilayer silicene is found similar to the monolayer one. The in-plane optical conductivity also shows the same results.

研究动机与目标

• 理解单层和双层硅烯在半导体-绝缘体相变点附近的电子输运特性。
• 分析自旋、谷和亚晶格自由度在电子散射与相变中的作用。
• 确定不同硅烯构型中从半导体到绝缘体相变的临界Hubbard U值。
• 研究带电杂质与库仑屏蔽对光学电导率和输运的影响。
• 探索强电子关联下反铁磁序与莫特绝缘体行为的出现。

提出的方法

• 采用多带紧束缚模型描述单层和双层硅烯的电子结构，包含最近邻（t）和次近邻（t'）跃迁积分。
• 在动量空间中推导出裸格林函数之间的散射矩阵，表明在弱耦合条件下单个杂质构型下具有动量无关性。
• 使用静态极化函数Π(k,Ω)的随机相位近似（RPA）计算，该函数在强耦合区域中对确定屏蔽库仑相互作用至关重要。
• 利用从狄拉克型哈密顿量和γ矩阵导出的速度算符（v_x, v_y, v_z）计算光学电导率。
• 通过涉及层间距离d的双曲正弦和余弦项的修正极化函数，对屏蔽层间Hubbard排斥进行建模。
• 通过调节局域Hubbard U分析相变，临界值通过反铁磁序和莫特绝缘体行为的出现来确定。

实验结果

研究问题

• RQ1 驱动单层硅烯从半导体到绝缘体相变的Hubbard U临界值是多少？
• RQ2 带电杂质的存在如何影响硅烯的光学电导率和电子输运？
• RQ3 RPA极化函数在确定硅烯中屏蔽库仑散射中的作用是什么？
• RQ4 为何AA堆叠双层硅烯需要更高的U值（12 eV）才能实现与单层硅烯（9 eV）相同的相变？
• RQ5 自旋-轨道耦合与亚晶格结构如何影响反铁磁序与莫特绝缘相的出现？

主要发现

• 在洁净单层硅烯中，半导体-绝缘体相变的临界Hubbard U为9 eV。
• 对于第二类AA堆叠双层硅烯或杂质强度为4 eV的单层硅烯，临界U为12 eV，表明对金属态具有更强的稳定性。
• 第一类AA堆叠双层硅烯表现出与单层硅烯相似的输运与相变行为，表明其电子响应相近。
• 光学电导率结果与相变临界值一致，证实了相变特征的稳健性。
• 带电杂质引发长程库仑散射，在零温极限下平均弹性扩散距离与√n成正比。
• 三重激发子的出现与d1+id2配对不稳定性与次近邻跃迁积分t'的减小有关，表明在临界U附近配对倾向增强。