Band alignment of two-dimensional semiconductors for designing heterostructures with momentum space matching

We present a comprehensive study of the band alignments of two-dimensional (2D) semiconducting materials and highlight the possibilities of forming momentum-matched type I, II, and III heterostructures, an enticing possibility being atomic heterostructures where the constituent monolayers have band edges at the zone center, i.e., $mathrm{ensuremath{Gamma}}$ valley. Our study, which includes the group IV and III-V compound monolayer materials, group V elemental monolayer materials, transition-metal dichalcogenides, and transition-metal trichalcogenides, reveals that almost half of these materials have conduction and/or valence band edges residing at the zone center. Using first-principles density functional calculations, we present the type of the heterostructure for 903 different possible combinations of these 2D materials which establishes a periodic table of heterostructures.