Double-resonant LA phonon scattering in defective graphene and carbon nanotubes

We present measurements of the $D''$ Raman mode in graphene and carbon nanotubes at different laser excitation energies. The Raman mode around 1050 - 1150\,cm$^{-1}$ originates from a double-resonant scattering process of longitudinal acoustic (LA) phonons with defects. We investigate its dependence on laser excitation energy, on the number of graphene layers and on the carbon nanotube diameter. We assign this Raman mode to so-called 'inner' processes with resonant phonons mainly from the $Γ-K$ high-symmetry direction. The asymmetry of the $D''$ mode is explained by additional contributions from phonons next to the $Γ-K$ line. Our results demonstrate the importance of inner contributions in the double-resonance scattering process and add a fast method to investigate acoustic phonons in graphene and carbon nanotubes by optical spectroscopy.

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