Kohn anomalies are kinks or dips in phonon dispersions which are pronounced in low-dimensional materials. We investigate the effects of nonadiabatic phonon self-energy on Kohn anomalies in one-dimensional metals by developing a model that analyzes how the adiabatic phonon frequency, electron effective mass, and electron-phonon coupling strength influence phonon mode renormalization. We introduce an electron-phonon coupling strength threshold for low-temperature system instability, providing experimentalists with a tool to predict them. Finally, we validate the predictions of our model against first-principles calculations on a 4 Å-diameter carbon nanotube.

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• Charge density waves
• Electron-phonon coupling
• Fermi surface
• First-principles calculations
• Nesting
• Peierls transition
• Phonons
• Nanotubes
• Nanowires
• Density functional theory