Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials

TL;DR

This paper derives comprehensive selection rules for phonon measurements in graphene, clarifies previous misunderstandings, and validates the rules through theoretical calculations and experimental HREELS data.

Contribution

It provides a complete set of symmetry-based selection rules for the honeycomb lattice, correcting prior literature and applying them to interpret HREELS measurements of graphene.

Findings

Derived complete selection rules for graphene's phonon spectrum.

Validated rules with HREELS measurements on graphene/Ru(0001).

Discussed effects of symmetry breaking scenarios.

Abstract

When the phonon spectrum of a material is measured in a scattering experiment, selection rules preclude the observation of phonons that are odd under reflection by the scattering plane. Understanding these rules is crucial to correctly interpret experiments and to detect broken symmetries. Taking graphene as a case study, in this work we derive the complete set of selection rules for the honeycomb lattice, showing that some of them have been missed or misinterpreted in the literature. Focusing on the technique of high-resolution electron energy loss spectroscopy (HREELS), we calculate the scattering intensity for a simple force constant model to illustrate these rules. In addition, we present HREELS measurements of the phonon dispersion for graphene on Ru(0001) and find excellent agreement with the theory. We also illustrate the effect of different symmetry breaking scenarios in the selection rules and discuss previous experiments in light of our results.