Scale-free ferroelectricity induced by flat phonon bands in HfO 2

cause extreme localization of electric dipoles within its irreducible half-unit cell widths (~3 angstroms). Contrary to conventional ferroelectrics with spread dipoles, those intrinsically localized dipoles are stable against extrinsic effects such as domain walls, surface exposure, and even miniaturization down to the angstrom scale. Moreover, the subnanometer-scale dipoles are individually switchable without creating any domain-wall energy cost. This offers unexpected opportunities for ultimately dense unit cell-by-unit cell ferroelectric switching devices that are directly integrable into silicon technology.