A symmetry based approach to evaluation of carbon nanotube electronic hyperpolarizability

The properties of the carbon nanotubes (CNTs) hyperpolarizability β due to π electrons is studied by using the formalism of the irreducible representations of CNT space symmetry group (G). The main contribution to the second order nonlinearity is demonstrated to come from electrons at the origin of the Brillouin zone (k=0). Within this scheme, a description based on the isogonal point group associated to G accounts for the relevant properties of β.