  The aim of this model study of the electron-phonon coupling in graphene was
to find out about the relative importance of the inter- and intraband
scattering and which phonon modes are the most active. This was achieved by
analyzing the electron-phonon matrix element of the carbon dimer in the unit
cell. We found that for the intra molecular orbital matrix elements the
longitudinal optical phonon mode is the active phonon mode. The matrix element
corresponding to sigma to sigma is greater than the matrix element for pi to pi
. The inter molecular orbital scattering pi to sigma is driven by the
out-of-plane acoustic phonon mode, while the out-of-plane optical mode does not
contribute for symmetry reasons. We found the unexpected result that the
magnitude of matrix element of the inter molecular orbital scattering pi to
sigmat exceeds the intra molecular orbital scattering pi to pi . These results
indicate that the in general not considered inter-band scattering has to be
taken into account when analyzing e.g. photo-hole lifetimes and the
electron-phonon coupling constant ?from photoemission data of graphene.
