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

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 similar to 1.4 nm are in resonance condition. In semiconducting nanotubes, the G(-)- and G(+)-mode frequencies increase by similar to 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 similar to 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 (similar to 18 cm(-1)) and D (similar to 10 cm(-1)) band for electron doping, whereas the 2D band remains constant for the hole doping but D upshifts by similar to 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.