Magic auxeticity angle of graphene

Solids exhibit transverse shrinkage when they are stretched, except auxetics that abnormally demonstrate lateral expansion instead. Graphene possesses the unique normal-auxeticity (NA) transition when it is stretched along the armchair direction but not along the zigzag direction. Here we report on the anisotropic temperature-dependent NA transitions in strained graphene using molecular dynamics simulations. The critical strain where the NA transition occurs increases with respect to an increase in the tilt angle deviating from armchair direction upon uniaxial loading. The magic angle for the NA transition is 10.9°, beyond which the critical strain is close to fracture strain. In addition, the critical strain decreases with an increasing temperature when the tilt angle is smaller than the NA magic angle. Our results shed lights on the unprecedented nonlinear dimensional response of graphene to the large mechanical loading at various temperatures.