Moiré-Induced Vibrational Coupling in Double-Walled Carbon Nanotubes

Moiré patterns are additional, long-range periodicities in twisted crystalline bilayers. They are known to fundamentally change the electronic states of the layers, but similar effects on their mechanical and vibrational properties have not been discussed so far. Here we show that the moiré potential shifts the radial breathing mode in double-walled carbon nanotubes (DWCNTs). The change in frequency is expected to be proportional to the shift in optical transition energies, which are induced by the moiré patterns. To verify our model, we performed resonance Raman scattering on purified and sorted semiconducting DWCNTs. We find that the radial breathing mode shifts up to 14 cm^-1 higher in energy followed by displacement of optical transition energies of up to 200 meV to lower energies, in comparison to the single-walled tubes. We show how to identify the strong coupling condition in DWCNTs from their phonon frequencies and construct a Kataura plot to aid their future experimental assignment.