Simulation the response of graphene to an external electric field using the exact tight-binding model

Numerical simulation of the interaction of electromagnetic radiation with graphene allows us to reproduce fast nonlinear processes and their observed manifestations. The paper presents the results obtained in the process of developing a software solution for calculating the observed parameters of such processes. In graphene physics, the massless fermion approximation is classical. However, in the study of processes with high energy density, model based on this approximation are beyond the limits of their applicability and the results obtained on their basis can not be considered reliable. To solve this problem, a transition to a substantially more accurate model based on a strict account of the nearest-neighbor interaction in the crystal lattice (tight-binding model) has been made. Comparative testing of these two models shows that at low energy characteristics of the external perturbation the results coincide. However, as the energy characteristics of the affecting electromagnetic field increase, the divergence of the results becomes apparent and grows. The new exact model has a more complex mathematical formulation and requires more computational resources. When using the same hardware configuration it is expressed in the increase of counting time. Relative and absolute values for a number of examples are given. The obtained results allow us to expand the range of parameters for modeling of nonlinear processes in the considered material, for example, generation of high-frequency harmonics and ensure its reliability. (In Russian).