The interaction of electron-hole pairs with lattice vibrations exhibits a wealth of intriguing physical phenomena. The Kohn anomaly is a renowned example where electron-phonon coupling leads to non-analytic phonon dispersion at specific momentum nesting the Fermi surface. Here we report evidence of another type of phonon anomaly discovered by low temperature Raman spectroscopy in bilayer graphene where the charge density is modulated by the electric field effect. This anomaly, arising from charge-tunable modulations of particle-hole pairs that are resonantly coupled to lattice vibrations, is predicted to exhibit a logarithmic divergence in the long-wavelength optical-phonon energy. In a non-uniform bilayer of graphene, the logarithmic divergence is abated by charge density inhomogeneity leaving as a vestige an anomalous phonon softening. The observed softening marks the first confirmation of the phonon anomaly as a key signature of the resonant deformation-potential electron-phonon coupling. The high sensitivity of the phonon softening to charge density non-uniformity creates significant venues to explore the interplay between fundamental interactions and disorder in the atomic layers.
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