  We calculate hybridization of plasmons and intrinsic optical phonons in
graphene by using the self-consistent linear response formalism. We find that
longitudinal plasmons (transverse magnetic modes) couple exclusively to
transverse optical phonons, whereas graphene's transverse plasmons (transverse
electric modes) couple only to longitudinal optical phonons. This mixing of
polarizations is in contrast to the usual plasmon-phonon coupling in other
systems. The resulting change in phonon frequencies increases (decreases) for
transverse (longitudinal) phonons by increasing the concentration of charge
carriers.
