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Ferroelectric materials are spontaneous symmetry breaking systems that are 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. In particular, the vibration polar wave has zero frequency gap, thus is constricted deeply inside ferroelectric domain wall, and can even propagate in the presence of local pinnings. The ferroelectric domain wall waveguide as demonstrated here offers a new paradigm in developing ferroelectric information processing units.

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