Universal Density of States for Carbon Nanotubes

Scanning tunneling microscopy (STM) and spectroscopy experiments have been recently reported for individual single-wall carbon nanotubes (SWNT) [1,2], confirming the strongly one-dimensional nature expected for the electron states in these materials [3,4]. The STM experiments give a direct experimental probe of the electron density of states (DOS) near the Fermi level. We have recently shown that semiconducting SWNTs with similar diameters will have similar DOS near the Fermi level, and established an analogous correspondence for metallic nanotubes [5]. We also gave expressions for the positions of the peaks near the Fermi level. Here we derive a universal relationship for the DOS in the vicinity of the Fermi level for SWNTs. This relationship, based on the graphene sheet model, scales out the dependence on the nanotube diameter and otherwise only depends on whether the SWNT belongs to the semiconducting or metallic groups of nanotubes. We compare the predictions of this relationship with the DOS results calculated using first-principles band structure results for SWNTs