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.
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