A symmetry based approach to evaluation of carbon nanotube electronic hyperpolarizability

摘要

The properties of the carbon nanotubes (CNTs) hyper polarizability β due to Π electrons is studied by using the formal ism of the irreducible representations of CNT space symmetry group (G). The main contribution to the second order nonlinear- ity is demonstrated to come from electrons at the origin pf the Brillouin zone (k = 0). Within this scheme, a description based on the isogonal point group associated to G accounts for the rel evant properties of β.