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

We investigate the relative importance of inter- and intraband scattering in Graphene and which phonon modes are the most active ones. The electron-phonon matrix element is analyzed for 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 to σ is greater than the matrix element for π to π. The inter molecular orbital scattering π to σ is driven by the out-of-plane acoustic phonon mode and surprisingly exceeds in intensity the intra molecular orbital scattering π to π. Below the matrix elements dependence of the inverse screening length α and the inter carbon distance R are shown.