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Ab-initio resonant Raman simulations in graphene, few layer graphene, and graphite

Multi-layer graphene with rhombohedral ABC stacking is considered as a promising carbon phase possibly displaying correlated states like magnetism or high-T c superconductivity due to the occurrence of an ultraflat electronic surface band at the Fermi level. Despite Bernal graphite being the most stable form of graphite, three and four layers graphene samples with rhombohedral stacking can be synthesized. Recently, flakes of thickness up to 17 layers were tentatively attributed ABC sequences although the Raman fingerprint of rhombohedral multilayer graphene is currently unknown and the 2D two-phonon resonant Raman spectrum of Bernal graphite not completely theoretically understood. Here we provide a complete first principles description of the 2D Raman peak in three and four layer graphene for all possible stackings, as well as for bulk Bernal, rhombohedral and an alternation of Bernal and rhombohedral graphite, that can be seen as a periodic sequence of ABA and ABC trilayers. Calculations for several laser energies are performed and we give practical prescriptions are proposed to identify long range sequences of ABC multi-layer graphene flakes.