Smyrnov O. Exciton excitations in carbon nanotubes

The model of large-radius exciton in a quasi-one-dimensional semiconductor has been developed within the long-wave and effective-mass approximations. The standard model of one-dimensional hydrogen-like system has been revised. On the basis of developed exciton model, for such quasi-one-dimensional semiconductors as single-walled carbon nanotubes, the spectra of excitons and general dependences of their characteristics on the nanotube parameters and the environment permittivity have been obtained taking into account different forms of the electron-hole interaction screening. The effect of single-electron spectrum instability with respect to exciton formation has been revealed for nanotubes in dielectric media with permittivity less than 1.8 (approximately). This effect leads to the partial destruction of single-electron states and their subsequent stabilization. Therefore, the band gap of a nanotube in vacuum should exceed the band gap of the same tube surrounded by medium with permittivity greater than 1.8. The obtained results are in good agreement with existing experimental data. The mentioned effects have been also revealed and studied by the example of simplest quasi-one-dimensional semiconductor – linear, diatomic crystal.