Interface-induced warping in hybrid two-dimensional materials

Two-dimensional hybrid materials consisting of heterogeneous domains have been of great interest. Using empirical molecular dynamical simulation, we show that the morphology of such hybrid 2D materials can extend into the third dimension via strong warping intrinsic to the interfaces between the domains. The interface warping stems from the compressive stress in the domain with a larger lattice constant and even penetrates into the stretched domain. Based on classic plate theory, we analytically quantify the amplitude, wave length and penetration depth of the interface warping as functions of the lattice mismatch, achieving good agreement with the simulations. Moreover, we propose that periodically placing pentagon-heptagon dislocations along the interface can eliminate the warping in the 2D material and such defective interface can be more favorable than the warped one over a critical domain size, which is consistent with recent experimental observations. Our results suggest that the interface warping in 2D hybrid materials should be considered in further exploring their promising properties.