Nonadiabatic Renormalization of the Phonon Dispersion in Monolayer and Bilayer Graphene

Nonadiabatic effects profoundly influence lattice dynamics, resulting in phonon renormalizations not only at the center of Brillouin zone (BZ), but also across the entire dispersion at finite momenta. These nonadiabatic phenomena exhibit clear dimensional dependencies and remain largely unexplored experimentally in low-dimensional systems. Here, we utilize high-resolution electron energy loss spectroscopy to investigate nonadiabatic phonon dispersion renormalization in monolayer graphene (MLG) and Bernal bilayer graphene (BLG). We present comprehensive phonon spectra measurements for both MLG and BLG across the full BZ. The high-resolution data reveal an intriguing "W" -shaped dispersion for the longitudinal optical phonon in MLG and a "V" -shaped dispersion in BLG near the BZ center, in contrast to the conventional "U" -shaped parabolic dispersions. Combining theoretical analysis, these anomalous phonon renormalizations are demonstrated to originate from nonadiabatic electron-phonon couplings. The comparative study of MLG and BLG gives a generic understanding of the impact of nonadiabatic effects on phonon dispersions in doped two-dimensional systems.