Impact of out-of-plane deformation on atomic reconstruction in twisted van der Waals bilayers

The effects of out-of-plane deformation on atomic relaxation in twisted van der Waals bilayers are investigated by comprehensive multiscale modeling and simulations. The model integrates the DFT-informed generalized stacking-fault energy for interlayer interaction between layers and the Föppl–von Kármán plate theory for elastic energy in each layer with minimization of the total free energy for atomic relaxation governed by a gradient flow method. Our simulation results elucidate twist-angle dependent moiré pattern, strain field, tortional displacement field and stacking domain structures, in good agreement with recent experimental observations. In particular, we derive the strain soliton solution at a small twist angle and the soliton free elastic solution at a large twist angle for the reconstructed van der Waals bilayer with out-of-plane deformation. These results show that out-of-plane deformation not only modifies the strain soliton width but also induces substantial alterations in the strain field, local rotation, and stacking structures. Our findings reveal the non-neglectable role played by out-of-plane deformation in the atomic relaxation of twisted van der Waals bilayers, particularly at smaller twist angles. The intricate interplay between in-plane atomic relaxation and out-of-plane deformation provides opportunities for strain engineering in twisted van der Waals bilayers.