Revealing Isotope Effects on Phonon Dispersion by Raman Imaging

Isotope substitution is widely used to probe phonon behavior in hydrogen-rich materials, yet its effects on phonon dispersion remain difficult to access and poorly understood, particularly in low-dimensional systems. Here, using trans-polyacetylene (t-PA) as a prototypical model, we theoretically demonstrate tip-enhanced Raman scattering (TERS) imaging as a real-space approach for visualizing isotope effects on phonon dispersion. To enable a complete comparison between hydrogenated and deuterated t-PA, we access all optical phonon branches by activating the normally Raman-forbidden out-of-plane modes through the field-gradient effect. The newly resolved out-of-plane branches exhibit a crossing after deuteration, arising from their distinct wavevector-dependent isotope responses. By introducing the hydrogen-site mass participation factor, we show that phonon modes with stronger hydrogen-site motion undergo larger isotope-induced red shifts, whereas its wavevector-dependent variation governs dispersion reshaping and branch crossing. Moreover, Raman images directly visualize the deuteration-induced redistribution of vibrational amplitudes associated with hydrogen-site motions, thereby revealing the microscopic origin of isotope effects on phonon dispersion. These findings establish TERS imaging as a powerful real-space approach for visualizing isotope-dependent phonon behavior in low-dimensional molecular systems.