Modern theory of polarization in ferroelectrics

Abstract Abstract 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 approach provides a powerful algorithm, which has been implemented in the framework of the first-principles theory of materials.