用cDFT研究了MSi（M = Cr，Mn，Fe，$\&$，Co）的电子结构，计算了$\textit{$ U_{eff}、PDMATHAAD、$\&$ $\textit{J}$
Investigating the electronic structure of MSi (M = Cr, Mn, Fe $\&$ Co) and calculating $\textit{$U_{eff}$}$ $\&$ $\textit{J}$ by using cDFT
摘要：
用密度泛函理论研究了金属间化合物$\textit{viz.}$ CrSi，MnSi，FeSi和CoSi的电子能带结构和分电子态密度。CrSi \MnSi、FeSi和CoSi分别具有金属、间接带隙半导体（带隙$ \sim$ 90 meV）和半金属基态。研究了穿过Cr-Co系时的能带结构，发现费米能级附近的占据带变窄，而未占据带变宽。类似地，部分态密度中的带边由于增加的杂化而远离费米能级。结果表明，FeSi中空穴的有效质量远大于电子的有效质量，导致了正的Seebeck系数和负的Hall系数，这与实验结果一致.对3-\textit{d} -金属的不同离子态，用约束DFT方法计算了$\textit{$、U_{eff}、$}$和$\textit{J}$的值.对于整个系列的$2^{+} $离子状态的$\textit{$ U_{eff} $\textit{J}$（$\textit{J}$）为$\sim $ 3.3 eV（$\sim $ 0.65 eV）、$\sim $ 3.7 eV（$\sim $ 0.72 eV）、$\sim $ 4.4 eV（$\sim $ 0.82 eV）和$\sim $ 4.5 eV（$\sim $ 0.87 eV）。考虑库仑相互作用的汤川形式，计算了$λ$和$\textit{J}$。$2^{+} $离子状态的$λ$值沿系列为$\sim $ 1.97 a。$u^{-1}$、$\sim $ 2.07 a. $u^{-1}$、$\sim $ 2.07 a. $u^{-1}$和$\sim $ 2.34 a. $u^{-1}$。发现4个$\textit{s}$电子在屏蔽3个$\textit{d}$电子方面比3个$\textit{d}$金属的4个$\textit{p}$电子贡献更大。
英文摘要：
We have investigated electronic energy band structures and partial density of states of intermetallic compounds $\textit{viz.}$ CrSi, MnSi, FeSi and CoSi, by using density functional theory (DFT). CrSi \& MnSi, FeSi and CoSi have metallic, indirect band gap semiconducting (band gap $ \sim$ 90 meV) and semi-metallic ground state, respectively. On studying the band structures while going across the series Cr-Co, the occupied bands around the Fermi level are getting narrower while the unoccupied bands are getting wider. Similarly, band edge in partial density of states is shifting away from the Fermi level due to increased hybridizations. The effective mass of holes for FeSi is found to be much larger than that of electrons, giving rise to positive Seebeck coefficient and negative Hall coefficient, which is consistent with experimental results. For different ionic states of 3\textit{d}-metal, the values of $\textit{$U_{eff}$}$ and $\textit{J}$ are evaluated by using constrained DFT method. $\textit{$U_{eff}$}$ ($\textit{J}$) for $2^{+} $ ionic state across the series are $\sim $ 3.3 eV ($\sim $0.65 eV), $\sim $ 3.7 eV ($\sim $0.72 eV), $\sim $ 4.4 eV ($\sim $ 0.82 eV) and $\sim $ 4.5 eV ($\sim $ 0.87 eV). $λ$ and $\textit{J}$ are also calculated by considering Yukawa form of Coulomb interaction. $λ$ values for $2^{+} $ ionic state along the series are $\sim $ 1.97 a.$u^{-1}$, $\sim $ 2.07 a.$u^{-1}$, $\sim $ 2.07 a.$u^{-1}$ and $\sim $ 2.34 a.$u^{-1}$. 4$\textit{s}$ electrons are found to be contributing more in screening the 3$\textit{d}$ electrons as compared to 4$\textit{p}$ electrons of 3$\textit{d}$ metals.
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