Revisiting Ferroelectricity Beyond Polar Space Groups

Abstract: Ferroelectricity, a hallmark of spontaneous inversion-symmetry breaking, has been a central concept in condensed matter physics and functional materials research, yet recent discoveries are revealing that switchable polarization can emerge in forms far richer than allowed by the conventional symmetry-based paradigm. Fractional quantum ferroelectricity and ionic-conductor ferroelectricity challenge the long-standing association of ferroelectricity exclusively with polar space groups. In this Review, we reconcile these emerging phenomena within the Berry-phase modern theory of polarization. We emphasize that polarization in insulating periodic crystals is not a single-valued vector, but a multivalued lattice quantity defined modulo a polarization quantum. Consequently, nonpolar crystals may possess nonzero formal polarization, and adiabatic paths connecting symmetry-equivalent structures can produce quantized changes in polarization without violating symmetry principles. The symmetry of this multivalued formal polarization is governed by a generalized Neumann principle. We further show that the large polarization changes induced by long-range ion migration in both fractional quantum ferroelectrics and ionic-conductor ferroelectrics can be naturally understood through the topological definition of oxidation state, which links ionic transport to quantized charge transfer and polarization change. We discuss the physical accessibility of these unconventional polarization states, highlighting the roles of switching pathways, boundary conditions, and domain-wall dynamics, particularly in systems such as $α$-In$_2$Se$_3$. Finally, we suggest that the most promising functionality of these materials may lie not in conventional bulk ferroelectric switching, but in the creation and control of charged interfaces and domain walls arising from discontinuities in formal polarization.