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Anomalous Optical Phonon Splittings in Sliding Bilayer Graphene

We study the variations of electron-phonon coupling and their spectroscopic consequences in response to sliding of two layers in bilayer graphene using first-principles calculations and a model Hamiltonian. Our study shows that the long wave-length optical phonon modes change in a sensitive and unusual way depending on the symmetry as well as the parity of sliding atomic structures and that, accordingly, Raman- and infrared-active optical phonon modes behave differently upon the direction and size of the sliding. The renormalization of phonon modes by the interlayer electronic coupling is shown to be crucial to explain their anomalous behavior upon the sliding. Also, we show that the crystal symmetry change due to the sliding affects the polarized Stokes Raman-scattering intensity, which can be utilized to detect tiny misalignment of graphene layers using spectroscopic tools.