Kohn Anomaly with Spin–Orbit Coupling in Monolayer Graphene: A Method to Determine the Rashba Parameter

The spin–orbit effect on the quantum corrections to the frequencies of the Γ-point optical phonon modes in graphene within the continuum approximation for phonons and the effective-mass approximation for electrons is first investigated theoretically. The phonon self-energy is calculated in the one-loop approximation, including electron–phonon interaction. The frequency shift and broadening of the optical phonon mode strongly depend on the strength of Rashba spin–orbit coupling (SOC) in graphene. We separately analyze phonon self-energy renormalization due to Rashba SOC and doping in monolayer (ML) graphene. We have obtained the renormalized phonon energy and the broadening of the optical phonon mode by an exact theoretical derivation of the phonon self-energy with Rashba spin–orbit coupling. The obtained results allow the determination of the Rashba SOC parameter values by experimentally studying the mentioned dependencies.