Origin and Evolution of Ultraflatbands in Twisted Bilayer Transition Metal Dichalcogenides: Realization of Triangular Quantum Dot Array

Abstract

Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS${}_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS${}_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($\theta$) close to 0${}^{\circ }$ and at both the valence and conduction band edges for $\theta$ close to 60${}^{\circ }$, and have distinct origins. For$\theta$ close to 0${}^{\circ }$, inhomogeneous hybridization in the reconstructed moiré superlattice is sufficient to explain the formation of flatbands. For $\theta$ close to 60${}^{\circ }$, additionally, local strains cause the formation of modulating triangular potential wells such that electrons and holes are spatially separated. This leads to multiple energy-separated ultraflatbands at the band edges closely resembling eigenfunctions of a quantum particle in an equilateral triangle well. Twisted bilayer transition metal dichalcogenides are thus suitable candidates for the realisation of ordered quantum dot array.

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