Non-vertical optical transition in near-field enhanced spectroscopy of graphene

We theoretically investigate the optical transition of an electron in graphene that is excited by near-field around a conical Au tip. The interaction between the near-field and the electron is calculated by tight-binding method. In the case of near-field, the wavevector of the electron changes by the optical absorption from the valence band to the conduction band. We show that the change of the wavevector is inversely proportional to the localization width of the near-field, which is given as a function of the distance between the tip and graphene. We calculate the near-field absorption probability as a function of k in the Brillouin zone. (paper)