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

Abstract

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.

Keywords:

• graphene
• electromagnetic waves
• Mathieu equation
• gaps

Acknowledgements

We thank CONACyT 48783-F, 50368 and DGAPA-UNAM project IN 100310-3. Calculations were carried at the KanBalam Supercomputer of UNAM.