  Electron-electron interactions and excitons in carbon nanotubes are locally
measured by combining Scanning tunneling spectroscopy and optical absorption in
bundles of nanotubes. The largest gap deduced from measurements at the top of
the bundle is found to be related to the intrinsic quasi-particle gap. From the
difference with optical transitions, we deduced exciton binding energies of 0.4
eV for the gap and 0.7 eV for the second Van Hove singularity. This provides
the first experimental evidence of substrate-induced gap renormalization on
SWNTs.
