The electron-phonon matrix element in the dirac point of graphene

The chief aim of this paper is to derive the matrix element of electron-phonon interaction in graphene as a function of phonon wave vector. The tight binding model, harmonic crystal approximation, and deformation potential approximation were employed for obtaining the matrix element. Required microscopic parameters are available in the current literature. This technique allows the most precise derivation of the electronphonon matrix element in graphene based on the semiempirical models. Scattering of electrons from the Dirac point is considered as most important. The 2D plots of the e-ph matrix element absolute value as a function of the phonon wave vector for in-plane modes are given as a result. These plots show the high anisotropy of the e-ph matrix element and singularities in high symmetry points. The results are in agreement with the long-wavelength approximation.