Interlayer Coupling and Strain Localization in Twisted Bilayer 2D Materials

Twisted bilayer 2D materials exhibit a wide range of intriguing physical properties, such as superconductivity, ferromagnetism, and superlubricity. Depending on the twist angle, periodic moire superlattices form in twisted bilayer graphene, with inhomogeneous interlayer coupling and lattice deformation. For a small twist angle, each moire supercell contains a large number of atoms (>10,000), making it computationally expensive for first-principles and atomistic modeling. In this work, a finite element method based on a continuum model is used to simulate the inhomogeneous interlayer and intralayer deformations of twisted bilayer graphene and MoS2. The van der Waals interactions between the 2D layers are described by a periodic potential energy function, whereas each 2D layer is treated as a continuum membrane with effective elastic properties. Our simulations show that structural relaxation and the induced strain localization are most significant at small twist angles, where the strain distribution is highly localized as shear strain solitons along the boundaries between neighboring domains of commensurate AB stacking. Moreover, it is found that there exist many metastable equilibrium configurations at particular twist angles, depending on the specimen size. The nonlinear mechanics of twisted bilayer 2D material is thus expected to be essential for understanding the strain distributions in the moire superlattices and the strain effects on other physical properties.