2019/11/30 by Ziyan Zhu, Paul Cazeaux, Mitchell Luskin +1
Chemistry · Materials Science · Physics and Astronomy · #2D Materials and Applications #Bilayer #Boron and Carbon Nanomaterials Research #Chemistry #Condensed matter physics #Energy minimization #Geometry #Graphene research and applications #Materials science #Physics #Quantum mechanics #Relaxation (psychology) #Stacking #Supercell #Superlattice #Twist #cond-mat.mes-hall #van der Waals force
paper · pdf · doi:10.1103/physrevb.101.224107
published as Phys. Rev. B 101, 224107 (2020)
openalex created_date 2019/11/22 · arxiv created 2020/04/20 · openalex publication_date 2020/06/08 · arxiv updated 2020/07/01 · openalex updated_date 2026/08/06
The incommensurate stacking of multilayered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multiscale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the need for commensurate approximations. To obtain the relaxation pattern, we perform energy minimization with respect to the relaxation displacement vectors. We use a continuum model in combination with the generalized stacking fault energy to describe the interlayer coupling, obtained from first-principles calculations based on density functional theory. We show that the relaxation patterns of twisted trilayer graphene and WSe2 are ``moir'e of moir'e,'' as a result of the incommensurate coupling two bilayer moir'e patterns. We also show that, in contrast to the symmetry-preserving in-plane relaxation in twisted bilayers, trilayer relaxation can break the two fold rotational symmetry about the xy plane when the two twist angles are equal.