Topological nature of polarization and charge pumping in ferroelectrics

Electric polarization in insulators is represented by the transferred charge through a shift of the Bloch wave functions induced by an adiabatic change of external parameters Q-->. It is found that this covalent/quantum contribution is determined nonlocally by the topological structure in the Q--> space. The condition for the charge pumping for a cyclic change of Q--> is also obtained. Applications of this picture to various organic ferroelectrics and BaTiO3 are discussed.