How to stack graphene and hBN on top of each other?

Question

I read in papers (e.g. link) about AA stacking, where C atoms are above the B and N atoms, and AB stacking where one C atom is above the N or B atom, while the other C atom is above the h-BN hexagon.

In this case, graphene stretches a little bit because of the 1.8% lattice mismatch.

However, in the Udemy course 'Building 2D Material Heterostructures in VESTA' (link), graphene and hBN are placed on each other by making a $\sqrt{28}$ supercell of graphene and $\sqrt{27}$ supercell of hBN. The resulting heterostructure looks like this:

It has a lattice mismatch of only 0.02%.

Which stacking to use in modelling? A simple AA or AB with 1.8% lattice mismatch or this one with a much lower lattice mismatch?

Which structure is actually obtained experimentally?

Answer 1

Whenever you stack two or more materials with different cell parameter, you have to create a commensurate supercell. In most cases the supercell will not exactly commensurate with all the materials and some stress will remain in at least one of the materials. The supercell used, as well as which of the materials to strain and to what extent is a choice that you have to make for you calculation as there is, strictly speaking, no universally correct answer.

As a rule of thumb it is common to assume that the less overall strain the better, so with this criterion in mind the structure with $0.02\%$ mismatch is the best choice. Often the computational resources limit the amount of atoms/electrons that you can calculate, so you should make sure that your resources are suitable for the less strained (and thus usually larger) supercell. Furthermore, even for structures with higher strain, you can choose the cell parameter to strain only the graphene, only the h-BN or to strain both layers. Nevertheless, the "correct" answer may also depend on the physics that you are interested in researching.

As for which structure is obtained experimentally - this is also an open question, as you will find experimental references for many stackings (besides the link in the question, a simple search finds this and this and of course many more). Once more the answer can depend on the physics that you are interested in.

It might help to compare your stackings and supercells to previously published calculations. For example here some stackings and twist angles are shown and the effect on the band structure, DOS, and more is explored.