Diameter dependence of TO phonon frequencies and the Kohn anomaly in armchair single-wall carbon nanotubes

Abstract

We present resonant Raman scattering experiments on nanotube samples enriched in metallic armchair single-wall carbon nanotubes (SWCNTs). We establish the transverse optical $({\mathcal{A}}_{\mathrm{TO}})$ phonon frequency for the (5,5) through (10,10) armchair species, ranging in diameter from 0.68 to 1.36 nm. The frequencies show a strong diameter dependence similar to that previously observed in semiconducting nanotubes. We show that the ${\mathcal{A}}_{\mathrm{TO}}$ frequencies in armchair SWCNTs are dramatically upshifted from those of semiconducting SWCNTs. Furthermore, using electrochemical doping, we demonstrated that the ${\mathcal{A}}_{\mathrm{TO}}$ frequencies in armchair SWCNTs are independent of the position of the Fermi level. These results suggest that the upshift is a result of a Kohn anomaly involving a forward-scattering mechanism of electrons close to the Fermi level. This is in contrast to the well-known Kohn anomaly that dominates the downshift of the ${\mathcal{A}}_{\mathrm{LO}}$ and ${\mathcal{E}}_{2g}$ phonons in nonarmchair metallic SWCNTs and graphene, respectively.