ABSTRACT
Graphene nanoribbons are quite different from carbon nanotubes in terms of quantum numbers, wave functions, energy gaps, state degeneracies, selection rules and magnetic field effects, clearly illustrating the critical role of the boundary conditions. The main features of absorption peaks strongly depend on the geometric structures of carbon nanotubes. Zigzag and armchair graphene nanoribbons, respectively, correspond to armchair and zigzag carbon nanotubes. The significant effects due to lateral quantum confinement and magnetic field clearly illustrate the dimension-diversified essential properties. The periodical boundary condition induces the decoupled angular-momentum states in carbon nanotubes, but the open boundary condition cannot create a transverse quantum number in a graphene nanoribbon. The distinct characteristics of subenvelope functions dominate the diverse selection rules, the conservation of angular momentum in carbon nanotubes, the same index of valence and conduction subbands in armchair nanoribbons and the index difference of odd integers in zigzag nanoribbons.
