Band alignment of lateral two-dimensional heterostructures with a transverse dipole

It was recently shown that the electronic band alignment in lateral two-dimensional heterostructures is strongly dependent on the system geometry, such as heterostructure width and layer thickness. This is so even in the absence of polar edge terminations because of the appearance of an interface dipole between the two different materials. In this study, this work is expanded to include two-dimensional materials that possess an electronic dipole over their surface, i.e., in the direction transverse to the crystal plane. To this end, a heterostucture consisting of polar hydrofluorinated graphene and non-polar graphane layers is studied with first-principles calculations. As for nonpolar heterostructures, a significant geometry dependence is observed with two different limits for the band offset. For infinitely wide heterostructures, the potential step in the vacuum is equally divided over the two sides of the heterostructure, resulting in a finite potential step in the heterostructure. For infinitely thick heterostructure slabs, on the other hand, the band offset is reduced, similar to the three-dimensional case.