Spontaneous curvature in two-dimensional van der Waals heterostructures

Two-dimensional (2D) van der Waals heterostructures consist of different 2D crystals with diverse properties, constituting the cornerstone of the new generation of 2D electronic devices. Yet interfaces in heterostructures inevitably break bulk symmetry and structural continuity, resulting in delicate atomic rearrangements and novel electronic structures. In this paper, we predict that 2D interfaces undergo "spontaneous curvature", which means when two flat 2D layers approach each other, they inevitably experience out-of-plane curvature. Based on deep-learning-assisted large-scale molecular dynamics simulations, we observe significant out-of-plane displacements up to 3.8 & Aring; in graphene/BN bilayers induced by curvature, producing a stable hexagonal moir & eacute; pattern, which agrees well with experimentally observations. Additionally, the out-of-plane flexibility of 2D crystals enables the propagation of curvature throughout the system, thereby influencing the mechanical properties of the heterostructure. These findings offer fundamental insights into the atomic structure in 2D van der Waals heterostructures and pave the way for their applications in devices.