Fractional quantum ferroelectricity.

For an ordinary ferroelectric, the magnitude of the spontaneous electric polarization is at least one order of magnitude smaller than that resulting from the ionic displacement of the lattice vectors, and the direction of the spontaneous electric polarization is determined by the point group of the ferroelectric. Here, we introduce a new class of ferroelectricity termed Fractional Quantum Ferroelectricity. Unlike ordinary ferroelectrics, the polarization of Fractional Quantum Ferroelectricity arises from substantial atomic displacements that are comparable to lattice constants. Applying group theory analysis, we identify 28 potential point groups that can realize Fractional Quantum Ferroelectricity, including both polar and non-polar groups. The direction of polarization in Fractional Quantum Ferroelectricity is found to always contradict with the symmetry of the "polar" phase, which violates Neumann's principle, challenging conventional symmetry-based knowledge. Through the Fractional Quantum Ferroelectricity theory and density functional calculations, we not only explain the puzzling experimentally observed in-plane polarization of monolayer α-InSe, but also predict polarization in a cubic compound of AgBr. Our findings unveil a new realm of ferroelectric behavior, expanding the understanding and application of these materials beyond the limits of traditional ferroelectrics.