Phonon Self-Energy Corrections to Nonzero Wave-Vector Phonon Modes in Single-Layer Graphene

Abstract

Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q=0) wave vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene originating from a double-resonant Raman process with q≠0. The observed phonon renormalization effects are different from what is observed for the zone-center q=0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons with nonzero wave vectors (q≠0) in single-layer graphene in which the frequencies and decay widths are expected to behave oppositely to the behavior observed in the corresponding zone-center q=0 processes. Within this framework, we resolve the identification of the phonon modes contributing to the G[superscript ⋆] Raman feature at 2450 cm[superscript -1] to include the iTO+LA combination modes with q≠0 and also the 2iTO overtone modes with q=0, showing both to be associated with wave vectors near the high symmetry point K in the Brillouin zone.