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

Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS₂ (TBLM), a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no special magic angles in TBLM. Ultraflatbands, which 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°, have distinct origins. For θ close to 0°, inhomogeneous hybridization in the relaxed moiré superlattice is sufficient to explain the formation of flatbands. For θ close to 60°, apart from the inhomogeneous hybridisation, 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 closely resembling eigenfunctions of a quantum particle in an equilateral triangle well.