Abstract

Atomically-thin layers of two-dimensional materials can be assembled in vertical stacks held together by van der Waals forces, allowing for coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation. A consequence of using these degrees of freedom is the emergence of a periodicity in the local atomic registry of the constituent crystal structures, known as a moiré superlattice. Here, we discuss the regimes for the formation of moiré SL in bilayers of transition metal dichalcogenides, distinguishing between the rigid-crystal behavior of the two layers and lattice reconstruction into perfect stacking domains (2H or 3R type, depending on the orientation of the layers), separated by the screw dislocation networks. For both of these two regimes, we discuss the effect of the superlattice on electronic and optical properties of various twisted TMD homo- and heterobilayers, including the tunneling characteristics, piezoelectricity effects in the strongly reconstructed bilayers, flat miniband formation for holes in twisted heterostructures, and the SL effects for the excitons.