六角形锗的多带 $k \cdot p$ 理论
Multiband $k \cdot p$ theory for hexagonal germanium
AI总结：
本研究针对六角形锗能带结构的未解问题，构建含自旋轨道耦合的多带$k\cdot p$模型，拟合ab initio数据得到有效质量等参数，解释偶极耦合弱的成因，推导低能哈密顿量并预测磁场下的g因子。
摘要：
六角形锗及其部分硅合金中发现的直接带隙，使得IV族半导体家族中出现了一种具有光学活性的材料，拥有多种潜在技术应用。然而，关于其能带结构的若干方面仍存在一些未解决的问题，包括布里渊区中心处电偶极跃迁的强度。我们利用Γ点附近的$\mathbf{k\cdot p}$方法（包含10个能带）并考虑自旋轨道耦合，通过拟合ab initio数据得到了一个自洽模型，该模型能产生正确的能带曲率以及此前未知的倒有效质量参数，用以描述2H-Ge，并计算电子和空穴的有效质量。为理解最低导带与最高价带之间较弱的偶极耦合，我们从无自旋12能带模型出发，证明当加入自旋轨道耦合时，最低导带会与位置更高的导带发生杂化，这一现象无法用含自旋的10能带模型解释。借助Löwdin划分方法，我们推导了导带的有效低能哈密顿量，可用于潜在的自旋动力学和纳米结构研究；同时以类似方式，给出了仅价带模型的最佳拟合参数，可用于输运研究。最后，利用自洽10能带模型，我们纳入了磁场的影响，并预测了导带和价带的电子与空穴g因子。
英文摘要：
The direct bandgap found in hexagonal germanium and some of its alloys with silicon allows for an optically active material within the group-IV semiconductor family with various potential technological applications. However, there remain some unanswered questions regarding several aspects of the band structiure, including the strength of the electric dipole transitions at the center of the Brillouin zone. Using the $\mathbf{k\cdot p}$ method near the $Γ$ point, including 10 bands, and taking spin-orbit coupling into account, we obtain a self-consistent model that produces the correct band curvatures, with previously unknown inverse effective mass parameters, to describe 2H-Ge via fitting to {\it ab initio} data and to calculate effective masses for electrons and holes. To understand the weak dipole coupling between the lowest conduction band and the top valance band, we start from a spinless 12-band model and show that when adding spin-orbit coupling, the lowest conduction band hybridizes with a higher-lying conduction band, which cannot be explained by the spinful 10-band model. With the help of Löwdin's partitioning, we derive the effective low-energy Hamiltonian for the conduction bands for the possible spin dynamics and nanostructure studies and in a similar manner, we give the best fit parameters for the valance-band-only model that can be used in the transport studies. Finally, using the self-consistent 10-band model, we include the effects of a magnetic field and predict the electron and hole g-factor of the conduction and valance bands.
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