Figure 4
Preserved scale-free ferroelectricity with nearly zero domain wall energy in the superlattice. (A) Phonon dispersion of the ferroelectric o'-phase of the superlattice along \(\Gamma \to Y\) has three flat phonon bands (highlighted with dashed red line, the deviation in the frequency of the flat band is less than \(10 c{m}^{-1}\)). (B–D) Eigenvectors of flat phonon bands at the \(\Gamma\)-point visualized in terms of atomic displacements in the unit cell of o'-phase. (E) Atomic structure of the thinnest possible domain in the superlattice along the y-direction (top), local and average polarization of this domain structure (bottom). (F) Energy landscape of domain wall motion along the y-direction in the superlattice, starting from a uniformly polarized structure (top-left corner inset) to a structure with two consecutive opposite polarized layers (top-right corner inset) in the superlattice (black open circles) and HfO2 (red open squares).
