Optical Properties of Carbon Nanotubes - Van Hove Singularities

Van Hove Singularities

Optical properties of carbon nanotubes derive from electronic transitions within one-dimensional density of states (DOS). A typical feature of one-dimensional crystals is that their DOS is not a continuous function of energy, but it descends gradually and then increases in a discontinuous spike. In contrast, three-dimensional materials have continuous DOS. The sharp peaks found in one-dimensional materials are called Van Hove singularities.

Van Hove singularities result in the following remarkable optical properties of carbon nanotubes:

• Optical transitions occur between the v₁ − c₁, v₂ − c₂, etc., states of semiconducting or metallic nanotubes and are traditionally labeled as S₁₁, S₂₂, M₁₁, etc., or, if the "conductivity" of the tube is unknown or unimportant, as E₁₁, E₂₂, etc. Crossover transitions c₁ − v₂, c₂ − v₁, etc., are dipole-forbidden and thus are extremely weak, but they were possibly observed using cross-polarized optical geometry.

• The energies between the Van Hove singularities depend on the nanotube structure. Thus by varying this structure, one can tune the optoelectronic properties of carbon nanotube. Such fine tuning has been experimentally demonstrated using UV illumination of polymer-dispersed CNTs.

• Optical transitions are rather sharp (~10 meV) and strong. Consequently, it is relatively easy to selectively excite nanotubes having certain (n, m) indices, as well as to detect optical signals from individual nanotubes.