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 K + and K − valleys in few-layer TMDCs. We perform high-field magneto-reflectance spectroscopy on WSe2, MoSe2, and MoTe2 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 k · 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 K + and 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 MoTe2, followed by MoSe2, and smallest for WSe2.

Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory

“…The g -factors of Q -momentum excitons (9.2–14.5) are similar to those of D 0 and , whereas excitons with the hole at Γ are predicted to have rather small g -factors (<5.8) except for the spin-unlike configuration with electron (9.8). As expected, the g -factors of intralayer excitons in BL WSe 2 are close to the values of the corresponding ML excitons 46 . In addition to intralayer excitons, the BL hosts interlayer counterparts (e.g., intralayer Q L and interlayer , intralayer Q U and interlayer , so on) that exhibit the same g -factors within our model, which neglects Coulomb corrections for intralayer and interlayer excitons.…”

Fine structure of K-excitons in multilayers of transition metal dichalcogenides

“…In this paper we present the theoretical outline (based on k · p approach [17,27,30,37]) and the experimental data (results of reflectance and magnetoreflectance measurements), which, in a consistent manner, unveil the nature of direct bandgap (K ± points) excitonic transitions in 2H-stacked S-TMDs multilayers. The geometry of 2H stacking, wherein each subsequent layer is 180 • rotated around previous one, induces interaction and hybridization of the Bloch states in K + /K − /K + .…”

“…Here n = v, c andḡ c andḡ v are the additional parameters which describe the magnetic dependent coupling between layers of the system [37]. In new basis, defined in the main part of the text, the full Hamiltonians H…”

Magneto-optics of layered two-dimensional semiconductors and heterostructures: Progress and prospects

“…Conduction and valence bands (CB and VB respectively) of a semiconductor undergo a Zeeman splitting under a magnetic field characterized by their effective g factors. The effective g factor of a carrier in a band is strongly influenced by the spin-orbit interaction-induced band mixing 68,[132][133][134][135] 87,104,[142][143][144][145][146] , transmittance 56,101,147 or photoconductivity spectroscopy 2,148 . Zeeman splitting in terms of circularly-polarized components is given as…”