Photon-Assisted Spectroscopy of Dirac Electrons in Graphene

The quantum Goos-Hanchen e ect in graphene is investigated. The Goos-Hanchen phase shift is derived by solving the Dirac eigenvalue di erential equation. This phase shift varies with the angle of incidence of the quasiparticle Dirac fermions on the barrier. Calculations show that the dependence of the phase shift on the angle of incidence is sensitive to the variation of the energy gap of graphene, the applied magnetic eld and the frequency of the electromagnetic waves. The present results show that the conducting states in the sidebands is very e ective in the phase shift for frequencies of the applied electromagnetic eld. This investigation is very important for the application of graphene in nanoelectronics and nanophotonics.