Measuring many-body effects in carbon nanotubes with a scanning tunneling microscope

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.