Analytic solution for electrons and holes in graphene under electromagnetic waves: Gap appearance and nonlinear effects

We find the exact solution of graphene carriers dynamics under electromagnetic radiation. To obtain the solution of the corresponding Dirac equation, we combine Floquet theory with a trial solution. Then the energy spectrum is obtained without using any approximation. We also prove that the energy spectrum presents a gap opening, which depends on the radiation frequency and electric wave intensity, whereas the current shows a strongly nonlinear behavior.

Figure 1

(Color online) Graphene lattice. Atoms in the $A$ sublattice are shown with different color than those in the $B$ sublattice. The vector $\mathbf{k}$ in which the electromagnetic field propagates and the electric-field vector $\mathbf{E}$ are shown.