To determine the effect of the substrate on the optical frequency ω_LO(Γ) of free-standing graphene, the problem of the adsorbed on a solid substrate dimer, consisting of two carbon atoms bound by direct (kinetic) t and indirect t_ind (through the state of the substrate) exchanges, is considered. It is shown that in the case of a semiconductor substrate, the resulting interaction is t+|t_ind|, which leads to a frequency ω_LO(Γ) shift by Δω_LO(Γ)>0 (red shift of the Raman G-peak) and a relative shift δ_LO(Γ)=Δω_LO(Γ)/ ω_LO(Γ)~|t_ind|/t. The numerical estimates of δ_LO(Γ) made for the 6H-SiC substrate are in good agreement with the experimental data. In the case of a transition metal substrate, it is shown that for metals with large effective masses of d-electrons (elements of the end of the 3d-series), a situation Δ_LO(Γ)<0 is possible (blue shift), which actually takes place for graphene formed on Ni(111). Here, however, the theoretical estimates of |δ_LO(Γ)| are underestimated. Keywords: direct and indirect exchange, longitude optical frequency, SiC and d-metal substrates.

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Дата начала обработки статистических данных - 27 января 2016 г.