Symmetry and selection rules in the Raman spectra of carbon nanotubes

摘要: The symmetry of achiral single-walled (n,0) and (n,n) carbon nanotubes (CNTs) was examined the frequencies types vibrations allowed in Raman spectra were calculated. vibrational spectrum evaluated as eigenvalues dynamical matrix at Γ-point Brillouin zone. selection rules for active estimated by values elements responsible intensities corresponding transitions. (n,n)-CNTs with even odd n are characterized five six vibrations, respectively. number (n,0)-CNTs is if eight odd. Detailed analysis results obtained presented (10,10)-CNT an example.