Ultraflat bands and shear solitons in Moir\'e patterns of twisted bilayer transition metal dichalcogenides

Ultraflat bands in twisted bilayers of two-dimensional materials have potential to host strong correlations, including the Mott-insulating phase at half-filling of the band. Using first principles density functional theory calculations, we show the emergence of ultraflat bands at the valence band edge in twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. The computed band widths, 5 meV and 23 meV for 56.5$^\circ$ and 3.5$^\circ$ twist angles respectively, are comparable to that of twisted bilayer graphene near 'magic' angles. Large structural transformations in the Moir\'e patterns lead to formation of shear solitons at stacking boundaries and strongly influence the electronic structure. We extend our analysis for twisted bilayer MoS$_2$ to show that flat bands can occur at the valence band edge of twisted bilayer WS$_2$, MoSe$_2$ and WSe$_2$ as well.