For Fe₂VAl the temperature-dependent Seebeck coefficient S(T) and electrical resistivity ρ(T) were calculated within the framework of density functional theory (DFT). The DFT calculations were extended in terms of a DFT/LDA+U approach with U − J values attributed to Fe-d-like states. For simulating the general features of the measured data, a large range of U − J values was scanned with U − J = 2.145 eV as the recommended value. For this value a very small negative indirect gap of E(X) − E(Γ) = −0.0093 eV is found, which is significantly reduced as compared to the DFT-GGA value of −0.164 eV. Charge transfer was derived by Bader's approach, resulting in a significant transfer of 0.75 electronic charges to each Fe atom from Al (1.03) and V (0.48). The pseudogap states around the Fermi energy were analyzed in detail in terms of density of states, band structures and charge density contours. These states almost exclusively govern S(T) and ρ(T). They have large dispersions and are centered at Γ and X. They consist of tails of localized V and Fe states dangling to the Al site. The dispersion of the band along the k space direction X–Γ was modelled in terms of a tight-binding ansatz, resulting in k-dependent matrix elements. From our DFT study, based on the findings for S(T) and ρ(T), it appears that Fe₂VAl has a very small negative indirect gap in the electronic structure. By fitting the temperature-dependent Seebeck coefficient within a parabolic band model, a tiny positive band gap of around 0.003 eV is revealed which qualitatively agrees with the DFT results.

中文翻译：

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全Heusler化合物Fe2VAl的电子拟带隙态和电子输运

对于Fe ₂ VAl，在密度泛函理论（DFT）的框架内计算了随温度变化的塞贝克系数S（T）和电阻率ρ（T）。DFT计算是根据DFT / LDA + U方法扩展的，其中U - J值归因于类Fe-d态。为了模拟测量数据的一般特征，扫描了大范围的U - J值，建议的U - J = 2.145 eV。对于此值，E（X）-E（Γ）= -0.0093 eV，与-0.164 eV的DFT-GGA值相比，该值显着降低。电荷转移是通过Bader方法得出的，导致0.75个电子电荷从Al（1.03）和V（0.48）大量转移到每个Fe原子。根据状态密度，能带结构和电荷密度等值线，详细分析了费米能量周围的伪能隙状态。这些状态几乎专门控制S（T）和ρ（T）。它们具有较大的分散度，并以Γ和X为中心。它们由悬挂在Al站点上的局部V和Fe状态的尾部组成。频段沿着ķ空间方向X - Γ被建模以紧密结合拟设而言，导致ķ依赖性矩阵元素。从我们的DFT研究中，基于S（T）和ρ（T）的发现，看来Fe ₂ VAl在电子结构中具有非常小的负间接间隙。通过在抛物线带模型中拟合温度相关的塞贝克系数，可以发现约0.003 eV的微小正带隙，从质量上与DFT结果吻合。