The electronic structure of layered van der Waals ferromagnet ${\mathrm{CrI}}_3$ is studied with self-consistent diagrammatic approaches beyond GW approximation. Considerable improvement in the calculated band gap as compared to the non-self-consistent $G_0{W}_0$ results has been found. Certain spectral features in the valence bands discovered recently by angle-resolved photoemission spectroscopy are reproduced better when we use full frequency-dependent self-energy. Density-functional theory and quasiparticle self-consistent GW method which are based on frequency-independent self-energy are unable to resolve these features. Nonlocality effects in the diagrams beyond GW approximation are large for both polarizability and self-energy. This finding can potentially have an impact on the development of methods like GW$+$dynamical mean field theory.

中文翻译：

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来自自洽顶点校正GW方法的范德华铁磁体CrI3的电子结构

层状范德华铁磁体的电子结构 ${铬}_3$使用超出GW近似的自洽图解方法进行研究。与非自洽相比，计算的带隙有相当大的改进$G_0{宽}_0$结果已经找到。当我们使用全频率相关的自能时，最近通过角分辨光发射光谱发现的价带中的某些光谱特征可以更好地再现。基于频率无关自能的密度泛函理论和准粒子自洽引力波方法无法解决这些问题。对于极化率和自能而言，超出GW近似值的图中的非局域性效应都很大。这一发现可能会对GW等方法的开发产生影响$+$动态平均场论。