Spin-dependent interactions in orbital-density-dependent functionals: Noncollinear Koopmans spectral functionals

The presence of spin-orbit coupling or noncollinear 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 noncollinear Koopmans-compliant functionals based on Wannier functions and density-functional perturbation theory, targeting accurate spectral properties in the quasiparticle approximation. Our noncollinear Koopmans-compliant theory involves functionals of four-component orbital densities that can be obtained from the charge and spin-vector densities of Wannier functions. We validate our approach on four emblematic nonmagnetic 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>WSe</a:mi><a:mn>2</a:mn></a:msub></a:math>, the cubic perovskite <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>CsPbBr</b:mi><b:mn>3</b:mn></b:msub></b:math>, and the ferromagnetic semiconductor <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>CrI</c:mi><c:mn>3</c:mn></c:msub></c:math>. 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. Published by the American Physical Society 2024