Graphene under perpendicular incidence of electromagnetic waves: Gaps and band structure

摘要

We study the energy spectrum for the problem of graphene's carriers under perpendicular incidence of electromagnetic waves. To obtain the spectrum, we solve the Dirac equation under such a field. Then a generalized Mathieu equation is obtained. The limiting cases of strong and weak fields, as well as long and short wavelengths, are analyzed. The energy spectrum is obtained numerically by using the Whittaker method, and a perturbation method is used to obtain the analytical separatrix curve between allowed and forbidden states. The energy spectrum presents bands, and a gap at the Fermi energy. The gap is linear on the electromagnetic wave intensity.