Origin and evolution of ultraflat bands in twisted bilayer transition metal dichalcogenides: Realization of triangular quantum dots
Mit H. Naik, S. Kundu, Indrajit Maity, Manish Jain
Abstract
Using a multiscale computational approach, we probe the origin and evolution of ultraflat bands in moir\'e superlattices of twisted bilayer $\mathrm{Mo}{\mathrm{S}}_{2}$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer $\mathrm{Mo}{\mathrm{S}}_{2}$ for flat-band formation. Ultraflat bands form at the valence band edge for twist angles ($\ensuremath{\theta}$) close to ${0}^{\ensuremath{\circ}}$ and at both the valence and conduction band edges for $\ensuremath{\theta}$ close to ${60}^{\ensuremath{\circ}}$, and have distinct origins. For $\ensuremath{\theta}$ close to ${0}^{\ensuremath{\circ}}$, inhomogeneous hybridization in the reconstructed moir\'e superlattice is sufficient to explain the formation of flat bands. For $\ensuremath{\theta}$ close to ${60}^{\ensuremath{\circ}}$, 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 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.