Universal analytic expression of electric-dipole matrix elements for carbon nanotubes (original) (raw)

This paper presents a universal analytic expression for electric-dipole matrix elements applicable to carbon nanotubes (CNs) with arbitrary chirality, particularly focusing on light polarized perpendicular to the nanotube axis. Previous methods have had limitations in terms of chirality applicability and transition categorization, while this work aims to overcome those challenges by deriving a fully analytic expression that simplifies for zigzag and armchair configurations. This expression allows for the investigation of linear and nonlinear optical properties of single-walled carbon nanotubes (SWCNTs) and contributes to the understanding of their polarization-dependent optical behavior.