Zeeman spectroscopy of excitons and hybridization of electronic states in few-layer WSe${}_2$, MoSe${}_2$ and MoTe${}_2$

Abstract

Monolayers and multilayers of semiconducting transition metal dichalcogenides (TMDCs) offer an ideal platform to explore valley-selective physics with promising applications in valleytronics and information processing. Here we manipulate the energetic degeneracy of the ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ valleys in few-layer TMDCs. We perform high-field magneto-reflectance spectroscopy on WSe${}_2$, MoSe${}_2$, and MoTe${}_2$ crystals of thickness from monolayer to the bulk limit under magnetic fields up to 30 T applied perpendicular to the sample plane. Because of a strong spin-layer locking, the ground state A excitons exhibit a monolayer-like valley Zeeman splitting with a negative $g$-factor, whose magnitude increases monotonically when thinning the crystal down from bulk to a monolayer. Using the $\mathbf{k}\cdot \mathbf{p}$ calculation, we demonstrate that the observed evolution of $g$-factors for different materials is well accounted for by hybridization of electronic states in the ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ valleys. The mixing of the valence and conduction band states induced by the interlayer interaction decreases the $g$-factor magnitude with an increasing layer number. The effect is the largest for MoTe${}_2$, followed by MoSe${}_2$, and smallest for WSe${}_2$. Keywords: MoSe${}_2$, WSe${}_2$, MoTe${}_2$, valley Zeeman splitting, transition metal dichalcogenides, excitons, magneto optics.

14 pages, 5 figures