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

TL;DR

This paper develops a continuum theory for moiré minibands in the valence bands of twisted $ ext{MoS}_2$ bilayers at the $ ext{Gamma}$-point, revealing unique lattice models and symmetry effects.

Contribution

It introduces a new continuum model for $ ext{Gamma}$-valley moiré bands in transition metal dichalcogenide bilayers, validated by ab initio calculations, highlighting emergent symmetries and distinct lattice models.

Findings

Low-energy $ ext{Gamma}$-valley moiré holes differ from K-valley counterparts.

First three bands form single-orbital honeycomb, two-orbital honeycomb, and single-orbital kagome models.

Emergent $D_6$ symmetry influences band structure and lattice models.

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.