Fig. 10: An introductory visualization to support the quantitative definitions detailed in the Methods section.

a The 3D view of the relaxed MoS₂/MoSe₂ vdWHS without interlayer twist. b Schematic of out-of-plane corrugation during geometry optimization using the coordinates of Mo atoms. \({Z}_{{\rm{ML}}}\) represents upward/downward height displacement of each constituting layer. The interlayer distance is defined as the distance between the two adjacent surfaces generated through interpolation. c The 3D view of atomic positions and the profile of the out-of-plane displacement \({Z}_{{\rm{ML}}}\) using Mo atoms, along with a 2D projection of the interlayer distance \(d\). d The out-of-plane displacement obtained by scanning the atomic height along the diagonal of the vdWHS, as indicated by the arrow in (c), alongside the interlayer distance and the average corrugation \({Z}_{{\rm{tbL}}}\) (the variation of the midpoint height of top and bottom layer relative to the midrange height of the entire structure). e Sketch of heterostructures with either in-phase or out-of-phase corrugation. A 0.015% strain is applied to each constituting layer for generating the bilayer model.