Indirect interaction of the carbon atoms as the origin of the epitaxial graphene frequencies shift
Davydov S.Ju.1
1Ioffe Institute, St. Petersburg, Russia
Email: Sergei_Davydov@mail.ru
To determine the effect of the substrate on the optical frequency ωLO(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 tind (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+|tind|, which leads to a frequency ωLO(Γ) shift by ΔωLO(Γ)>0 (red shift of the Raman G-peak) and a relative shift δLO(Γ)=ΔωLO(Γ)/ ωLO(Γ)~|tind|/t. The numerical estimates of δLO(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 ΔLO(Γ)<0 is possible (blue shift), which actually takes place for graphene formed on Ni(111). Here, however, the theoretical estimates of |δLO(Γ)| are underestimated. Keywords: direct and indirect exchange, longitude optical frequency, SiC and d-metal substrates.
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