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The dynamical charges measure the macroscopic polarization induced by a relative sublattice displacement in a polar insulator. When the material has a mixed ionic/covalent character such charges present nontrivial features. Apparently similar oxides have strikingly different behaviors: some (like the ferroelectric perovskites) have giant dynamical charges, while others (like ZnO) are quite normal and display dynamical charges close to the nominal static ones. The rationale for such differences is found, upon closely scrutinizing the covalence mechanism. Furthermore, the effects of electron-electron interaction on the polarization of a model highly correlated dielectric are discussed.

Recently, the Berry's phase approach has made the macroscopic polarization of ferroelectric perovskites accessible to full quantum-mechanical treatment. First-principle calculations for KNbO3 have demonstrated—amongst other things—the overwhelming importance of asymmetric Nb-O bond length variations: such variations drag a giant macroscopic current across the sample during the ferroelectric distortion. Here we investigate the microscopic mechanism mostly responsible for such giant currents. It is shown that only the highest (so-called O2p) electronic bands significantly contribute to the polarization; furthermore evidence is given that a sizeable hydridization between the O2p oxygen orbitals and the Nb 4d orbitals occurs, this hybridization being the sole responsible for the giant currents.

A modern theory of the macroscopic electric polarization has been recently founded. Polarization itself is not an observable, while the polarization difference ΔP between any two crystal states can be measured, defined, and calculated as a bulk material property. An hysteresis cycle measures ΔP as the integrated current flowing through the sample: the present theory provides an expression for exactly this quantity. Being a current, ΔP is a property of the phases of the crystal wavefunctions, which can be cast as a Berry's phase, i.e. as a gauge-invariant phase feature of the valence Bloch orbitals. I stress that the periodic charge density of the polarized crystal-where any phase information is deleted-is irrelevant to macroscopic polarization. The present viewpoint elucidates the fundamental quantum nature of polarization: no Clausius-Mossotti-like model applies whenever the valence electrons are delocalized, as is the case in perovskites. Besides its conceptual importance, the Berry's phase app...

Contrary to common textbook statements, the macroscopic electric polarization of a crystal cannot be unambiguously defined as the dipole of a unit cell. The only measurable quantities are either derivatives of the polarization (dielectric susceptibility, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). The differential concept is a basic one in theoretical work too. I sketch here the basic theory and the state of the art in its implementation to real materials, both for induced and spontaneous polarization; for the latter case, I also propose a novel approach.