Emergent Moiré Effects on Vibrational Properties of Double-Walled Carbon Nanotubes

The radial-breathing–like modes (RBLMs) of double-walled carbon nanotubes (DWNTs) are phonons whose frequency depends sensitively on inter-wall interactions and on coupling with the environment. Previous theoretical models have primarily considered van der Waals interaction in describing these modes. In this work, we construct a reciprocal-space approach that incorporates an effective potential arising from moiré-induced modifications of the band structure, enabling a systematic treatment of moiré effects that conventional models cannot capture. Our analysis shows that for weakly coupled chiral pairs the frequency shifts remain extremely small and can be regarded as negligible, whereas under strong coupling conditions the moiré effect produces RBLM frequency shifts that are large enough to be experimentally detectable. Our approach advances the understanding of interlayer interactions in DWNTs, and enables their improved characterization by Raman spectroscopy. Furthermore, it provides a basis for the refinement of DWNT-based environmental sensing.