Abstract:
To determine the effect of the substrate on the optical frequency $\omega_{\mathrm{LO}}(\Gamma)$ 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 $t_{\mathrm{ind}}$ (through the state of the substrate) exchanges, is considered. It is shown that in the case of a semiconductor substrate, the resulting interaction is $t+|t_{\mathrm{ind}}|$, which leads to a frequency $\omega_{\mathrm{LO}}(\Gamma)$ shift by $\Delta\omega_{\mathrm{LO}}(\Gamma)>$ 0 (red shift of the Raman G-peak) and a relative shift $\delta_{\mathrm{LO}}(\Gamma)\equiv\Delta\omega_{\mathrm{LO}}(\Gamma)/\omega_{\mathrm{LO}}(\Gamma)\approx|t_{\mathrm{ind}}|/t$. The numerical estimates of $\delta_{\mathrm{LO}}(\Gamma)$ made for the 6$H$-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 $\Delta_{\mathrm{LO}}(\Gamma)<$ 0 is possible (blue shift), which actually takes place for graphene formed on Ni(111). Here, however, the theoretical estimates of $|\delta_{\mathrm{LO}}(\Gamma)|$ are underestimated.
Keywords:direct and indirect exchange, longitude optical frequency, SiC and $d$-metal substrates.
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