First-principles determination of the Raman fingerprint of rhombohedral graphite

Multilayer graphene with rhombohedral stacking is a promising carbon phase possibly displaying correlated states like magnetism or superconductivity due to the occurrence of a flat surface band at the Fermi level. Recently, flakes of thickness up to 17 layers were tentatively attributed to ABC sequences although the Raman fingerprint of rhombohedral multilayer graphene is currently unknown and the 2D resonant Raman spectrum of Bernal graphite is not understood. We provide a first principles description of the 2D Raman peak in three and four layers graphene (all stackings) as well as in Bernal, rhombohedral, and an alternation of Bernal and rhombohedral graphite. We give practical prescriptions to identify long range sequences of ABC multilayer graphene. Our work is a prerequisite to experimental nondestructive identification and synthesis of rhombohedral graphite.