Multiscale Green’s functions for modeling graphene and other Xenes

We give a review of the multiscale Green’s function method for modeling modern two-dimensional nanomaterials such as graphene and other Xenes. The method is applicable to materials at different space and time scales and is computationally efficient. This method is actually a generalized Green’s function method, which gives the response of a multiparticle system to a probe and is a powerful technique for solving a variety of problems in science and engineering. In the static case, the method can seamlessly link the length scales from atomistic to continuum in an integrated formalism. The multiscale nature of the static Green’s function is largely determined by the underlying Bravais lattice of a solid, which is the same for graphene and other Xenes. This allows us to treat graphene as a special case of Xenes. For time-dependent problems, we calculate a causal Green’s function by using the Laplace transform technique, which ensures causality. It can simulate physical processes in a multiparticle system over a wide range of time extending from femtoseconds to microseconds. For illustration, the static method is applied to simulate elastic deformation due to a point defect, such as a monovacancy, in graphene and silicene. For time-dependent problems, we illustrate the causal Green’s function method to simulate propagation of elastic waves in two-dimensional graphene.