Far-infrared gaps in single-wall carbon nanotubes

Reflectance of single-wall carbon nanotubes (SWNTs) has been measured over 15-30000 cm(-1) (2-3720 meV). The sample is a free-standing film composed o f purified SW`NTs. The temperature dependence of the reflectance is quite s mall at all temperatures studied (7.8 K to 298 K) and no vibrational featur es are observed. The spectra have a Drude-like dispersion, the reflectance monotonically decreasing as photon energy increases, with a plasma edge aro und 2500 cm(-1) (310 meV). The dispersion is analyzed by a Drude model comb ined with a low-frequency localized band. The optical conductivity derived from a Kramers-Kronig analysis shows a strong peak at 135 cm(-1) (17 meV), which corresponds to the Lorentzian absorption in the dispersion analysis. This far-infrared band is assigned to a pseudogap in metallic armchair nano tubes and/or to small-gaps in zigzag or chiral nanotubes. The sum-rule calc ulation indicates that the one third of SWNTs in our sample belongs to the class of metallic or small-gap SWNTs. Tbe lineshape of the far-infrared con ductivity is explained by an effective medium approximation to calculate th e dielectric function for the mixture of metallic and semiconducting SWNTs.