Model study of the electron-phonon coupling in graphene; relative importance of intraband and interband scattering

Abstract

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 σ→σ is greater than the matrix element for π→π. The inter molecular orbital scattering π→σ 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 π→σ exceeds the intra molecular orbital scattering π→π. 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 λ from photoemission data of graphene.