Global k -space analysis of electron-phonon interaction in graphene and application to M -point spectroscopy

Recently, optical probes have become available that can access and observe energy renormalization due to electron-phonon interaction in graphene away from the well-studied Dirac K point. Using an expanded deformation potential approach, we present a theoretical study of the electron-phonon self-energy and scattering matrix elements across the entire Brillouin zone. We elucidate the roles of modulated hopping and conventional deformation potential coupling, parameterized via standard deformation potentials, the in-plane phonon modes, intra- and interband contributions, and umklapp processes. Applying the theory to nonlinear optical transmission spectroscopy in the vicinity of the M point, we find very good agreement with recently published experimental data.