Gap opening and large spin-orbit splitting in MX2 (M=Mo,W X=S,Se,Te) from the interplay between crystal field and hybridizations: insights from ab-initio theory

Abstract

By means of first-principles density functional calculations, we study the maximally localized Wannier functions for the 2D transition metal dichalcogenides MX2 (M=Mo,W X=S,Se,Te). We found a M^+4-like ionic charge and a single occupied d-band. The center of the d-like maximally localized Wannier function associated with this band is distributed among three M sites. Part of the energy gap is opened by the crystal field splitting induced by the X^-2-like atoms. We extract the hopping parameters for the Wannier functions and provide a perspective on tight-binding model. From the analysis of the tight binding model, we have found an inversion of the band character between the Gamma and the K points of the Brillouin zone due to the M-M hybridization. The consequence of this inversion is the closure of the gap. The M-X hybridization is the only one that tends to open the gap at every k-point, the change in the M-X and M-M hybridization is the main responsible for the difference in the gap between the different dichalcogenide materials. The inversion of the bands gives rise to different spin-orbit splitting at Gamma and K point in the valence band. The different character of the gap at Gamma and K point offers the chance to manipulate the semiconductive properties of these compounds. For a bilayer system, the hybridizations between the out of plane orbitals and the hybridizations between the in plane orbitals split the valence band respectively at the Gamma and K point. The splitting in the valence band is opened also without spin-orbit coupling and comes from the M-M and X-X hybridization between the two monolayers.

References in corpus (6)

• Electric Field Effect in Atomically Thin Carbon Films
• Two Dimensional Atomic Crystals
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• A systematic study of structural, electronic and optical properties of atomic scale defects in 2D transition metal dichalcogenides MX${}_2$ (M = Mo,W; X = S, Se, Te)
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• A tight-binding model for MoS${}_2$ monolayers

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