  We theoretically study various aspects of the electron-surface optical phonon
interaction effects in graphene on a substrate made of polar materials. We
calculate the electron self-energy in the presence of the surface
phonon-mediated electron-electron interaction focusing on how the linear chiral
graphene dispersion is renormalized by the surface phonons. The electron
self-energy as well as the quasiparticle spectral function in graphene are
calculated, taking into account electron-polar optical phonon interaction by
using a many body perturbative formalism. The scattering rate of free electrons
due to polar interaction with surface optical phonons in a dielectric substrate
is calculated as a function of the electron energy, temperatures, and carrier
density. Effects of screening on the self-energy and scattering rate are
discussed. Our theory provides a comprehensive quantitative (and qualitative)
picture for surface phonon interaction induced many-body effects and hot
electron relaxation in Dirac materials.
