Intrinsic radial breathing oscillation in suspended single-walled carbon nanotubes

Radial breathing mode (RBM) oscillation is the most characteristic vibration mode in carbon nanotubes. Here we investigate the intrinsic behavior of RBM oscillations of structurally defined single-walled carbon nanotubes (SWNTs) by combining Raman-scattering and electron-diffraction techniques on the same suspended nanotubes. The independent determination of RBM frequencies and nanotube structures allows us to establish conclusively the perfect linear relation between RBM frequencies and inverse nanotube diameters, which has been long speculated to hold in pristine SWNTs. Understanding the intrinsic diameter dependence of SWNT RBM oscillation not only is crucial for reliable Raman characterization of carbon nanotubes, but also enables quantitative probing of SWNT-environment interactions through the RBM oscillation frequency shift.