First principles prediction of 2D lattice coherency in van der Waals heterostructures

Beginning with graphene-hBN van der Waals (vdW) heterostructures [1], many Moiré patterns between 2D materials have been observed [2,3]. Still, predicting the coherent, semi-coherent (Moiré) or incoherent matching of 2D lattices at their interface is a challenge for Density Functional Theory (DFT), due to the very large size of the supercells needed in such studies. We introduce a first-principles-based model that bypass the need for large supercells. It generalizes the well-known Frenkel-Kontorova model [4] by including physical effects present in real materials, as derived from a perturbative approach to the problem. In particular, a mean-field modification of the 2D lattice parameters and elastic constants appears, even if the matching of the lattices is incoherent. The results are compared to plain DFT computations and to experimental observations of lattice accommodation in vdW-heterostructures. Then, we predict lattice (in)coherency for a set of 36 vdW-heterostructures based on graphene, phosphorene and different transition metal dichalcogenides.
[1] C. Woods et al. Nat. Phys. 10, 451 (2014).
[2] C. Zhang et al. Sci. Adv. 3, e1601459 (2017).
[3] Y. Liu et al. Nat. Nanotechnol. 10, 1038 (2018).
[4] Y. I. Frenkel and T. Kontorowa. Zh. Eksp. Teor. Fir. 8, 1340 (1938).