Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals

The presence of spin-orbit coupling or non-collinear magnetic spin states can have dramatic effects on the ground-state and spectral properties of materials, in particular on the band structure. Here, we develop non-collinear Koopmans-compliant functionals based on Wannier functions and density-functional perturbation theory, targeting accurate spectral properties in the quasiparticle approximation. Our non-collinear Koopmans-compliant theory involves functionals of four-component orbitals densities, that can be obtained from the charge and spin-vector densities of Wannier functions. We validate our approach on four emblematic non-magnetic and magnetic semiconductors where the effect of spin-orbit coupling goes from small to very large: the III-IV semiconductor GaAs, the transition-metal dichalcogenide WSe₂, the cubic perovskite CsPbBr₃, and the ferromagnetic semiconductor CrI₃.
The predicted band gaps are comparable in accuracy to state-of-the-art many-body perturbation theory and include spin-dependent interactions and screening effects that are missing in standard diagrammatic approaches based on the random phase approximation. While the inclusion of orbital- and spin-dependent interactions in many-body perturbation theory requires self-screening or vertex corrections, they emerge naturally in the Koopmans-functionals framework.

材料中自旋轨道耦合或非共线磁自旋态的存在，对基态及其光谱性质产生显著影响，尤其是在能带结构方面。本研究基于Wannier函数和密度泛函微扰理论，发展了非共线Koopmans兼容泛函，旨在在准粒子近似下准确预测光谱性质。我们的非共线Koopmans兼容理论涉及四分量轨道密度泛函，这些泛函可以通过Wannier函数的电荷和自旋矢量密度获得。我们以四种标志性的非磁性及磁性半导体为验证对象，这些材料中自旋轨道耦合效应从微弱到极强不等：III-IV族半导体GaAs、过渡金属二硫族化合物WSe₂、立方钙钛矿CsPbBr₃以及铁磁半导体CrI₃。预测的能带间隙与最先进的许多体微扰理论在精度上相当，包括标准基于随机相位近似法的图解方法中缺失的与自旋相关的相互作用和屏蔽效应。尽管在许多体微扰理论中引入轨道和自旋相关的相互作用需要自屏蔽或顶点校正，但在Koopmans泛函框架中，这些相互作用自然出现。