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

Discovery of robust yet reversibly switchable electric dipoles at reduced dimensions is critical in advancing nanoelectronics devices. Energy bands flat in momentum space generate robust localized states that are activated independently of each other. We determined flat bands exist and induce robust yet independently switchable dipoles exhibiting a unique ferroelectricity in HfO2 Flat polar phonon bands in HfO2 cause extreme localization of electric dipoles within its irreducible half-unit-cell-widths (~3 Å). Contrary to conventional ferroelectrics with spread dipoles, those intrinsically localized dipoles are stable against extrinsic effects such as domain walls, surface exposure, and even down-to-angstrom-scale miniaturization. Moreover, the sub-nm-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 directly integrable into silicon technology.