Effect of electron correlations on theFe3Siandα−FeSi2band structure and optical properties

Abstract

We use the Vienna ab initio simulation package (vasp) for evaluation of the quasiparticle spectra and their spectral weights within Hedin's $\text{GW}$ approximation (GWA) for ${\text{Fe}}_{3}\text{Si}$ and $\ensuremath{\alpha}{\text{-FeSi}}_{2}$ within the non-self-consistent one-shot approximation ${\text{G}}_{0}{\text{W}}_{0}$ and self-consistent $\text{scGWA}$ with the vertex corrections in the particle-hole channel, taken in the form of two-point kernel. As input for ${\text{G}}_{0}{\text{W}}_{0}$, the band structure and wave functions evaluated within the generalized gradient corrected local-density approximation to density functional theory (GGA) have been used. The spectral weights of quasiparticles in these compounds deviate from unity everywhere and show nonmonotonic behavior in those parts of bands where the delocalized states contribute to their formation. The ${\text{G}}_{0}{\text{W}}_{0}$ and scGWA spectral weights are the same within 2%\char21{}5%. The scGWA shows a general tendency to return ${\text{G}}_{0}{\text{W}}_{0}$ bands to their GGA positions for the delocalized states, while in the flat bands it flattens even more. Variable angle spectroscopic ellipsometry measurements at $T=296$ K on grown single-crystalline $\ensuremath{\sim}50$-nm-thick films of ${\text{Fe}}_{3}\text{Si}$ on $n$-Si(111) wafer have been performed in the interval of energies $\ensuremath{\omega}\ensuremath{\sim}(1.3\char21{}5)$ eV. The comparison of ${\text{G}}_{0}{\text{W}}_{0}$ and $\text{scGW}$ theory with experimental real and imaginary parts of permittivity, refractive index, extinction and absorption coefficients, reflectivity, and electron energy loss function shows that both ${\text{G}}_{0}{\text{W}}_{0}$ and $\text{scGW}$ qualitatively describe experiment correctly, the position of the low-energy peaks is described better by the $\text{scGW}$ theory, however, its detailed structure is not observed in the experimental curves. We suggest that the angle-resolved photoemission spectroscopy experiments, which can reveal the fine details of the quasiparticle band structure and spectral weights, could help to understand (i) if the scGWA with this type of vertex correction is sufficiently good for description of these iron silicides and, possibly, (ii) why some features of calculated permittivity are not seen in optical experiments.