  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.
