Phonon-assisted indirect transitions in angle-resolved photoemission spectra of graphite and graphene

Abstract

Indirect transitions of electrons in graphene and graphite are investigated by means of angle-resolved photoemission spectroscopy (ARPES) with several different incident photon energies and light polarizations. The theoretical calculations of the indirect transition for graphene and for a single crystal of graphite are compared with the experimental measurements for highly-oriented pyrolytic graphite and a single crystal of graphite. The dispersion relations for the transverse optical (TO) and the out-of-plane longitudinal acoustic (ZA) phonon modes of graphite and the TO phonon mode of graphene can be extracted from the inelastic ARPES intensity. We find that the TO phonon mode for k points along the Γ-K and K-M-K′ directions in the Brillouin zone can be observed in the ARPES spectra of graphite and graphene by using a photon energy ≈11.1 eV. The relevant mechanism in the ARPES process for this case is the resonant indirect transition. On the other hand, the ZA phonon mode of graphite can be observed by using a photon energy ≈6.3 eV through a nonresonant indirect transition, while the ZA phonon mode of graphene within the same mechanism should not be observed.