Valley Zeeman Effect in 2D Transition Metal Dichalcogenides from First Principles

The Zeeman effect of excitons in two-dimensional transition metal dichalcogenides (TMDs) has attracted much recent attention. A g-factor can be associated with the valley splitting of the band structure in the presence of a weak out-of-plane magnetic field. Experimentalists have measured g-factors of -4 and -16 for excitons in monolayer and twisted bilayer TMDs. Theoretical interpretations of the g-factors have largely focused on monolayer TMDs, relying on a phenomenological model or a k.p model. The phenomenological model assumes that the g-factor is a sum of orbital, spin and valley terms, while the k.p model uses effective masses extracted from tight-binding calculations. Here, we start from the Luttinger-Kohn approximation to treat the magnetic field as a perturbation in a periodic system, and show that the g-factor cannot be written as a sum of only orbital, spin and valley terms. We compute the g-factors for TMD materials using density functional theory (DFT) and include self-energy corrections within many-body perturbation theory (MBPT). Using these results, we comment on the exciton g-factors measured in both monolayer and twisted bilayer TMDs, and show that the MBPT results agree better with experiment than DFT. The effects of spin-orbit coupling are also discussed.