  Ferroelectric materials are spontaneous symmetry breaking systems
characterized by ordered electric polarizations. Similar to its ferromagnetic
counterpart, a ferroelectric domain wall can be regarded as a soft interface
separating two different ferroelectric domains. Here we show that two bound
state excitations of electric polarization (polar wave), or the vibration and
breathing modes, can be hosted and propagate within the ferroelectric domain
wall. Specially, the vibration polar wave has zero frequency gap, thus is
constricted deeply inside ferroelectric domain wall, and can propagate even in
the presence of local pinnings. The ferroelectric domain wall waveguide as
demonstrated here, offers new paradigm in developing ferroelectric information
processing units.
