论文标题
在紧张的MG2X中，机器学习模型哈密顿和自旋轨道相互作用的强度（X = SI，GE，SN，PB）
Machine-learned model Hamiltonian and strength of spin-orbit interaction in strained Mg2X (X = Si, Ge, Sn, Pb)
论文作者
论文摘要
已经开发了机器学习的多轨道紧密结合（MMTB）汉密尔顿模型，以描述金属间化合物的电子特性$ \ rm MG_2SI，MG_2GE，MG_2SN $和$ \ rm mg_2pb $。 MMTB模型结合了自旋轨道介导的相互作用，并通过大量平行的多维蒙特 - 卡洛搜索算法校准通过密度功能理论（DFT）计算得出的电子带结构。结果表明，机器学习的五波段紧密结合模型再现了整个布里群区域中价带结构的关键方面。五波段型号揭示了压缩应变将$ 3S $宝质的$ \ rm米克$ $ \ rm米的贡献定位为$ \ rm x〜（x = si，ge，ge，sn，pb）$ $ \ rm p $ P $轨道对价乐队的贡献。相比之下，拉伸应变具有相反的效果，因为它削弱了$ 3S $轨道的$ \ rm米克$和外壳$ p $ p $ orbitals $ \ rm x $的贡献，分别对传导带和价带的贡献。与$σ$键合组件相比，$ \ rm mg_2x $化合物中的$π$键合可忽略不计，$σ$键合组件遵循层次结构$ |σ_{sp} |> | = |σ_{pp} |> |> | = |σ_{ss} | $，以及对应变的最大变化属于$ $ = $ $ = $} pp。五波段模型允许以$ \ rm mg_2x $估算自旋轨道耦合（SOC）的强度，并获得其对$ \ rm x $和应变的原子数的依赖性。此外，频带结构计算表明，由于应变而导致的显着带隙调谐和带状分裂。 $ -10 \％$的压缩应变可以以$γ$ $ \ rm \ rm \ rm的mg_2pb $打开带隙，而$+10 \％$的拉伸应变截止了$ \ rm mg_2si $的半导体带隙。 $+5 \％$的拉伸应变消除了$γ$ point $ \ rm \ rm \ rm mg_2ge $的$γ$点的三重变性。
Machine-learned multi-orbital tight-binding (MMTB) Hamiltonian models have been developed to describe the electronic characteristics of intermetallic compounds $\rm Mg_2Si, Mg_2Ge, Mg_2Sn$, and $\rm Mg_2Pb$ subject to strain. The MMTB models incorporate spin-orbital mediated interactions and they are calibrated to the electronic band structures calculated via density functional theory (DFT) by a massively parallelized multi-dimensional Monte-Carlo search algorithm. The results show that a machine-learned five-band tight-binding model reproduces the key aspects of the valence band structures in the entire Brillouin zone. The five-band model reveals that compressive strain localizes the contribution of the $3s$ orbital of $\rm Mg$ to the conduction bands and the outer shell $p$ orbitals of $\rm X~(X=Si,Ge,Sn,Pb)$ to the valence bands. In contrast, tensile strain has a reversed effect as it weakens the contribution of the $3s$ orbital of $\rm Mg$ and the outer shell $p$ orbitals of $\rm X$ to the conduction bands and valence bands, respectively. The $π$ bonding in the $\rm Mg_2X$ compounds is negligible compared to the $σ$ bonding components, which follow the hierarchy $|σ_{sp}|>|σ_{pp}|>|σ_{ss}|$, and the largest variation against strain belongs to $σ_{pp}$. The five-band model allows for estimating the strength of spin-orbit coupling (SOC) in $\rm Mg_2X$ and obtaining its dependence on the atomic number of $\rm X$ and strain. Further, the band structure calculations demonstrate a significant band gap tuning and band splitting due to strain. A compressive strain of $-10\%$ can open a band gap at the $Γ$ point in metallic $\rm Mg_2Pb$, whereas a tensile strain of $+10\%$ closes the semiconducting band gap of $\rm Mg_2Si$. A tensile strain of $+5\%$ removes the three-fold degeneracy of valence bands at the $Γ$ point in semiconducting $\rm Mg_2Ge$.
