Temperature Dependence of the Optical Transition Energies of Carbon Nanotubes: The Role of Electron-Phonon Coupling and Thermal Expansion

Tunable Raman spectroscopy is used to measure the optical transition energies $E_{ii}$ of individual single wall carbon nanotubes. $E_{ii}$ is observed to shift down in energy by as much as 50 meV, from $-160$ to 300 °C, in contrast with previous measurements performed on nanotubes in alternate environments, which show upshifts and downshifts in $E_{ii}$ with temperature. We determine that electron-phonon coupling explains our experimental observations of nanotubes suspended in air, neglecting thermal expansion. In contrast, for nanotubes in surfactant or in bundles, thermal expansion of the nanotubes’ environment exerts a nonisotropic pressure on the nanotube that dominates over the effect of electron-phonon coupling.

Figure 1

Radial breathing mode intensity of an individual suspended SWNT plotted as a function of laser energy for three different temperatures. The solid lines show theoretical fits to the experimental data. The peak intensities at each temperature are normalized for better graphical representation.

Figure 2

Calculated shifts in the transition energies $E_{ii}$ due to electron-phonon coupling for metallic ($E_{11}$) and semiconducting ($E_{22}$) nanotubes.