Renormalization of the phonon spectrum in semiconducting single-walled carbon nanotubes studied by Raman spectroscopy

Abstract

In situ Raman experiments together with transport measurements have been carried out in single-walled carbon nanotubes as a function of electrochemical top gate voltage (V_g). We have used the green laser (E_L=2.41 eV), where the semiconducting nanotubes of diameter ~1.4 nm are in resonance condition. In semiconducting nanotubes, the G⁻- and G⁺-mode frequencies increase by ~10 cm⁻¹ for hole doping, the frequency shift of the G⁻ mode is larger compared to the G⁺ mode at the same gate voltage. However, for electron doping the shifts are much smaller: G⁻ upshifts by only ~2 cm⁻¹ whereas the G⁺ does not shift. The transport measurements are used to quantify the Fermi-energy shift (E_F) as a function of the gate voltage. The electron-hole asymmetry in G⁻ and G⁺ modes is quantitatively explained using nonadiabatic effects together with lattice relaxation contribution. The electron-phonon coupling matrix elements of transverse-optic (G⁻) and longitudinal-optic (G⁺) modes explain why the G⁻ mode is more blueshifted compared to the G⁺ mode at the same V_g. The D and 2D bands have different doping dependence compared to the G⁺ and G⁻ bands. There is a large downshift in the frequency of the 2D band (~18 cm⁻¹) and D (~10 cm⁻¹) band for electron doping, whereas the 2D band remains constant for the hole doping but D upshifts by ~8 cm⁻¹. The doping dependence of the overtone of the G bands (2G bands) shows behavior similar to the dependence of the G⁺ and G⁻ bands.