Band alignment of transition metal dichalcogenide heterostructures

Two-dimensional heterostructures and superlattices consisting of transition metal dichalcogenides offer huge potential in the next generation of optoelectronic devices. For such transition metal dichalcogenides, a predictive theory of their properties, based upon in-depth understanding of the interlayer interactions, is desirable due to the huge potential number of combinations. These weakly interacting heterobilayers provide an excellent case study to understand how interlayer interactions interfere with the Anderson/Schottky picture of band alignment at interfaces. We demonstrate here, using a combination of first principles and tight-binding methods, how the band alignment can be predicted in terms of a modified form of Anderson's rule. We explain how two physically based corrections to Anderson's rule, Delta E-Gamma and Delta E-IF, are necessary for accurate band alignment prediction. We identify the interlayer interactions that affect band alignment prediction and show how these take the form of long range interactions between the d(z2) and/or p(z) orbitals and induced fields between layers. Finally, we apply this theorem to Moire and strained structures to predict these structures band alignment and provide a comprehensive guide to accurately predict the resultant band gap of the various transition metal dichalcogenide heterostructures.