$\Gamma$-Valley Transition-Metal-Dichalcogenide Moir\`e Bands

Abstract

The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $\Gamma$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moir\`e minibands that are formed in the valence bands of $\Gamma$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $\Gamma$-valley moir\`e holes differ qualitatively from their K-valley counterparts addressed previously; in energetic order the first three bands realize i) a single-orbital model on a honeycomb lattice, ii) a two-orbital model on a honeycomb lattice, and iii) a single-orbital model on a kagome lattice.