Theory of electronic ferroelectricity

We present a theory of the linear and nonlinear optical characteristics of the insulating phase of the Falicov-Kimball model within the self-consistent mean-field approximation. The Coulomb attraction between the itinerant $d$ electrons and the localized $f$ holes gives rise to a built-in coherence between the $d$ and $f$ states, which breaks the inversion symmetry of the underlying crystal, leading to (1) electronic ferroelectricity, (2) ferroelectric resonance, and (3) a nonvanishing susceptibility for second-harmonic generation. As experimental tests of such a built-in coherence in mixed-valent compounds, we propose measurements of the static dielectric constant, the microwave absorption spectrum, and the dynamic second-order susceptibility.