Flat bands in twisted bilayer transition metal dichalcogenides

Using scanning tunnelling spectroscopy, the flat bands in twisted bilayer WSe(2)are shown near both 0 degrees and 60 degrees twist angles. The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moire pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of 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(1-6). In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moire wavelengths over a range of twist angles around 0 degrees and 60 degrees (ref.(4)) 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 degrees and 57.5 degrees twisted bilayer WSe(2)samples using scanning tunnelling spectroscopy. Our direct spatial mapping of wavefunctions at the flat-band energy show that the localization of the flat bands is different for 3 degrees and 57.5 degrees, in agreement with first-principles density functional theory calculations(4).