Temperature-dependent electronic excitations of carbon toroids

Carbon toroids could exhibit rich inter-π-state and intra-π-state excitations at finite temperature. The low-frequency electronic excitations are characterized by the longitudinal angular momentum (L), mainly owing to the cylindrical symmetry. The L-decoupled plasmons strongly depend on temperature, toroid geometry, and intertoroid Coulomb coupling. Temperature could make the inter-π-state plasmons change into the intra-π-state plasmons, or directly induce the intra-π-state plasmons. It is very novel that temperature does not affect excitation spectra of armchair carbon toroids, such as plasmon peak and plasmon frequency. There are certain important differences between armchair and nonarmchair carbon toroids. Intertoroid Coulomb interactions for coaxial carbon toroids have been included. They significantly enhance plasmon peak and plasmon frequency. The low-frequency plasmons in a carbon toroid quite differ from the purely temperature-induced plasmons in a graphite sheet.