Band structure calculations of van der Waals heterostructures

Layer by layer stacking of two-dimensional materials gives rise to “van der Waals” (vdW) heterostructures of nanometer thickness and clean interfaces. These systems often exhibit extraordinary properties and present novel challenges for theory. Superconductivity of twisted bilayer graphene at the magic angle, interlayer excitons in transition metal dichalcogenide (TMD) heterostructures, and optoelectronic properties of TMD/graphene heterostructures, are examples, among others, where vdW heterostructures significantly differ from their monolayer constituents. We present density functional theory (DFT) results for the atomic and electronic structure of vdW heterostructures consisting of combinations of TMD monolayers and graphene. Due to the large size of the supercells used, DFT calculations are demanding and need careful interpretation. We have developed a methodology for unfolding and analyzing their electronic band structure. Interlayer interactions have been carefully included. Our results show that composition of monolayers, twist angles, and stress in the heterostructures have a strong influence on their observable optoelectronic properties.