Irreducible sub-nm2 ferroelectric domains by 2D-flat polar band in perovskite superlattices

Flat polar phonon bands in ferroelectrics have been envisioned to realize irreducibly small domains for achieving the highest memory density. However, such bands are quite uncommon, with only a one-dimensional flat polar band discovered in ferroelectric hafnia, which gives rise to irreducibly narrow, line-type domains with a half-unit-cell width of 2.7 Å. Here, we report the discovery of a two-dimensional flat polar band in the ferroelectric (BaTiO 3 ) 1 /(BaXO 3 ) 1 superlattice (X = Zr, Sn), which generates extremely localized, noninteracting dipoles within its quarter-unit-cell area that form quasi-degenerate states of irreducible sub-nm² ferroelectric domains. The estimated ferroelectric domain density, exceeding 300 \({{\mathrm{Tbit}}}/{{\mathrm{cm}}}^2\) (assuming one bit per domain) represents a record high among the known ferroelectrics, with independently switchable dipoles at low voltages. The ferroelectric phase hosting two-dimensional flat bands constitutes a competing ground state across superlattice stacking directions and thus can be experimentally realized in both freestanding structures and epitaxial growth on MgO substrates. This discovery opens unprecedented opportunities to explore multidimensional flat polar bands in ferroelectrics and to engineer ultra-dense and low-power memory devices.