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A metallic (semiconducting) single-wall nanotube contains an irrational (integral) number of carbon hexagons in the pitch. The room-temperature conductivity is higher by two to three orders of magnitude in metallic nanotubes than in semiconducting nanotubes. Tans et al. [Nature386 (1997) 474] measured the electrical currents in metallic single-wall carbon nanotubes under bias and gate voltages, and observed non-Ohmic behaviors. The original authors interpreted their data in terms of a ballistic transport due to the Coulomb blockage on the electron-carrier model. The mystery of why a ballistic electron is not scattered by impurities and phonons is unexplained, however. An alternate interpretation is presented based on the Cooper pair (pairon)–carrier model. Superconducting states are generated by the Bose–Einstein condensation of the ± pairons at momenta 2πℏn/L, where L is the tube length and n a small integer. As the gate voltage changes the charging state of the tube, the superconducting states jump between different n. The normal current peak shapes appearing in the transition are found to be temperature-dependent, which is caused by the electron–optical phonon scattering.

As the complex transmission coefficient for a Fabry–Perot dielectric plate is well-known, the density of states (DOS) approach by J. Bendickson et al. [Phys. Rev. E53, 4107 (1996)] was applied to the plate and a formula was found for the spectrum of its threshold gain for lasing from the dye-doped plate. Next, the dispersion relation and the spectrum of the threshold gain was discussed for the infinite helical cholesteric liquid crystal (CLC). Then the DOS approach was applied to the non-absorbing CLC layers having finite, different thickness. The threshold gain spectra were calculated and dependences were found of the minimum threshold gain on the layer thickness and the optical anisotropy of the material. Finally, the results of the DOS analytical technique were compared with numerical calculations based on the precise solutions of the Maxwell equations and, in such a way, the DOS technique has been proven. The contribution of the dye absorption was discussed separately. The experimental data presented in the paper are in good agreement with the threshold gain calculations.

Single-walled carbon nanotubes (SWNTs) synthesized by catalytic decomposition of an alcohol were purified by extraction. The purified SWNTs were characterized on the basis of visible-near infrared (vis-NIR) absorption, photoluminescence and Raman spectroscopic analyses, scanning electron microscopy (SEM) observation, and thermal analysis. Selective extraction of metallic nanotubes was also achieved by the extraction condition.