Atomic reconstruction enabled coupling between interlayer distance and twist in van der Waals bilayers

Achieving precise control over interlayer interactions and properties in van der Waals (vdW) bilayers represents a significant breakthrough in materials science. In this study, using molecular dynamic and a hybrid model we show an emergent coupling between interlayer distance and twist angle in the reconstructed twisted bilayer graphene (tBLG). The reconstructed state of tBLG arises from the delicate interplay between vdW interlayer interactions and elastic energy within each layer, leading to the emergence of a cross term in the average total energy density of tBLG concerning interlayer distance and twist angle. Such cross term enables tunable interlayer distance via twist and local rotation via interlayer distance. The average interlayer distance in tBLG undergoes an increase from 3.37 Å to 3.45 Å within the range of twist angles from 0° to 4°. Our investigation unveils that the coupling originates from regions of high-energy stacking with maximum interlayer distance increase with the twist angle due to atomic reconstruction. This coupling phenomenon is not exclusive to tBLG, as it appears in other vdW bilayers like MoS₂/MoS₂, MoSe₂/MoSe₂, WS₂/WS_2, and WSe₂/WSe₂. The coupled interlayer interaction between interlayer distance and twist would have implications for tailoring 2D vdW materials for various applications.