Electron-electron scattering rates in moderate-gap toroidal carbon nanotubes

The π -electronic excitations and deexcitations in moderate-gap zigzag (m,0,p,-2p) toroidal carbon nanotubes are investigated by employing the random phase approximation and Fermi's golden rule. The low-frequency intra- π -state e-h excitations are the effective de-excitation channels of the excited electrons. The inelastic electron-electron scattering rates depend sensitively on the state index l, height, temperature, and type of zigzag TCN. The state with l=p has the largest scattering rate. The thicker the torus is, the faster the excited electrons will decay. The decay rates grow rapidly with rising temperature. The calculated results can be verified by ultrafast optical measurements.