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Vertically stacked van der Waals heterostructures made of two-dimensional compounds are almost an infinite playground for the fabrication of nano-engineered materials for the most diverse applications. Unfortunately, high-throughput electronic structure theory, which often serves as a guidance for material design, is not practical in this case. In fact, the compositional and structural complexity of van der Waals heterostructures make the number of prototypes to calculate combinatorially large. In this work a method is developed to compute the bandstructure of van der Waals heterostructures with an arbitrary composition and geometry using minimal computational resources. Such scheme is applied to the systematic study of a library of two-dimensional hexagonal  X  Y  2  compounds. The method is based on the density functional theory and on the assumption that the inter-layer electronic interaction is limited to classical electrostatic screening. Our analysis enables us to identify and categorize a large range of van der Waals bilayer heterostructures with electronic band gaps of different nature ranging from 0.1 to 5.5 eV and various types of band line-up.

High-throughput bandstructure simulations of van der Waals hetero-bilayers formed by 1T and 2H monolayers