Probing zone-boundary optical phonons in doped graphene

We use first-principles density-functional theory to determine the adiabatic frequency shift of the A(1)(')-K and E-'-K phonons in a monolayer graphene as a function of both electron and hole doping. Compared to the results for the E-2g-Gamma phonon (Raman G band), the results for the A(1)(')-K phonon are dramatically different, while those for the E-'-K phonon are not so different. Furthermore, we calculate the frequency shifts, as a function of the charge doping of the (K+Delta K) phonons responsible for the Raman 2D band-a key fingerprint of graphene, where parallel to Delta K parallel to is determined by the double-resonance Raman process.