Origin and evolution of ultraflat bands in twisted bilayer transition metal dichalcogenides: Realization of triangular quantum dots

Using a multiscale computational approach, we probe the origin and evolution of ultraflat bands in moir\'e superlattices of twisted bilayer MoS₂, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS₂ for flat-band formation. Ultraflat bands form at the valence band edge for twist angles (θ) close to 0^∘ and at both the valence and conduction band edges for θ close to 60^∘, and have distinct origins. For θ close to 0^∘, inhomogeneous hybridization in the reconstructed moir\'e superlattice is sufficient to explain the formation of flat bands. For θ close to 60^∘, 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 ultraflat bands 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 realization of ordered quantum dot array.