Band energy landscapes in twisted homobilayers of transition metal dichalcogenides

Twistronic assembly of 2D materials employs the twist angle between adjacent layers as a tuning parameter for designing the electronic and optical properties of van der Waals heterostructures. Here, we study how interlayer hybridization, weak ferroelectric charge transfer between layers, and a piezoelectric response to deformations set the valence and conduction band edges across the moiré supercell in twistronic homobilayers of MoS2, MoSe2, WS2, and WSe2. We show that, due to the lack of inversion symmetry in the monolayer crystals, bilayers with parallel (P) and antiparallel (AP) unit cell orientations display contrasting behaviors. For P-bilayers at small twist angles, we find band edges in the middle of triangular domains of preferential stacking. In AP-bilayers at marginal twist angles ( θ A P < 1 °), the band edges are located in small regions around the intersections of domain walls, giving highly localized quantum dot states.