Flat bands in twisted bilayer transition metal dichalcogenides

The crystal structure of a material creates a periodic potential that electrons move through giving rise to the electronic band structure of the material. When two-dimensional materials are stacked, the twist angle between the layers becomes an additional degree freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moir\'e wavelengths over a range of twist angles around 0 and 60 degrees giving much wider versatility than magic angle twisted bilayer graphene. Here we show the existence of a flat band in the electronic structure of 3{\deg} and 57.5{\deg} twisted bilayer WSe2 samples using scanning tunneling spectroscopy. Direct spatial mapping of wavefunctions at the flat band energy have shown that the flat bands are localized differently for 3{\deg} and 57.5{\deg}, in excellent agreement with first-principle density functional theory calculations.