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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• Tuning flat bands by interlayer interaction, spin-orbital coupling, and external fields in twisted homotrilayer MoS${}_2$
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• Chiral Flat-Band Optical Cavity with Atomically Thin Mirrors
• Dynamic Valley Polarization in Moire Quantum Dots
• Extremely high excitonic $g$-factors in 2D crystals by alloy-induced admixing of band states
• Magnetoexcitons and Massive Dirac Fermions in Monolayers of Transition Metal Dichalcogenides in a High Magnetic Field
• Ab initio Approach to Collective Excitations in Excitonic Insulators