Valley Zeeman effect and Landau levels in Two-Dimensional Transition Metal Dichalcogenides

Abstract

This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the valley extrema in TMDs, energy bands split into Landau levels with a Zeeman shift in the presence of a uniform out-of-plane external magnetic field. The Landau level indices are symmetric in the $K$ and $K^{\prime }$ valleys. We develop a numerical approach to compute the single band g-factors from first principles without the need for a sum over unoccupied bands. Many-body effects are included perturbatively within the GW approximation. Non-local exchange and correlation self-energy effects in the GW calculations increase the magnitude of single band g-factors compared to those obtained from density functional theory. Our first principles results give spin- and valley-split Landau levels, in agreement with recent optical experiments. The exciton g-factors deduced in this work are also in good agreement with experiment for the bright and dark excitons in monolayer WSe${}_2$, as well as the lowest-energy bright excitons in MoSe${}_2$-WSe${}_2$ heterobilayers with different twist angles.

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• Optical properties of charged excitons in two-dimensional semiconductors
• Excitons in mesoscopically reconstructed moiré heterostructures
• Moiré excitons in MoSe${}_2$-WSe${}_2$ heterobilayers and heterotrilayers
• Exciton g-factors in monolayer and bilayer WSe${}_2$ from experiment and theory
• Moiré and beyond in transition metal dichalcogenide twisted bilayers
• Measurement of Conduction and Valence Bands g-factors in a Transition Metal Dichalcogenide Monolayer
• Magnetooptics of layered two-dimensional semiconductors and heterostructures: progress and prospects
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Charge transfer and asymmetric coupling of MoSe${}_2$ valleys to the magnetic order of CrSBr
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• Chirality of Valley Excitons in Monolayer Transition-Metal Dichalcogenides
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