Measurements on quantum capacitance of individual single walled carbon nanotubes

We report measurements of the quantum capacitance of individual semiconducting and small band gap single walled carbon nanotubes (SWNTs). The observed quantum capacitance, 82 aF/$\mu $m for a semiconducting SWNT with chiral index (16,8) and 10.3 aF/$\mu $m for a small band gap SWNT upon Fermi level lying at the first subband are remarkably smaller than those originating from the density of states. We attribute the discrepancy to a strong electron correlation in SWNTs and derive the Luttinger parameter $g $of 0.25--0.3 for the (16,8) SWNT and of 0.32 for a small band gap SWNT.