Mechanics of out-of-plane screw dislocation in a 2D material

We study the mechanics of out-of-plane screw dislocations in two-dimensional (2D) materials using elastic membrane theory and atomistic simulations. Through elastic membrane theory, we derive a closed-form equation for the excess energy of the out-of-plane screw dislocation, revealing that the strain associated with the dislocation in a 2D material diminishes more rapidly with distance compared to that in a bulk material. We utilize this equation to compute energy profiles of out-of-plane screw dislocations in graphene. Various core radii across Burgers vectors (i.e., number of layers) under conditions with and without hydrogen termination on the dislocation core are considered, and computed energies are validated by atomistic simulations. Our results show that the screw dislocation core has a finite core radius which increases as the Burgers vector increases to avoid a high stress concentration at the dislocation core, thereby minimizing the total energy. Furthermore, we extend our theory to include the interaction between screw dislocations in a dipole configuration. Simulation results indicate that the relaxation narrows a high-strain concentration region near the dislocation core, where the interaction energy becomes negligible. Additionally, we examine the influence of out-of-plane screw dislocations on alternating twisted multilayer graphene. Our results reveal that the screw dislocation induces additional in-plane strain on the structure near the dislocation core, but that this additional strain is confined to within 2 nm of the dislocation core.