  We study the Magneto-Electric (ME) effect from the viewpoint of the Berry
phase connection and quantum adiabatic charge transport (QAPT). The linear
response theory for the electronic polarization $\vec{P}_{\rm{el}}$ can be
interpreted in terms of the flux or the fictitious magnetic field related to
the Berry phase in the generalized space which is composed of a crystal
momentum and some external parameters. An applied magnetic field modifies the
spin configuration, which induces adiabatic deformation of the Bloch
wavefunction and results in the electronic polarization given by the total flux
penetrating the plaquette spanned by this external parameter and crystal
mometum. This provides a new mechanism for the gigantic ME effect. For a cyclic
change of the applied magnetic field, even a quantized charge transport is
possible.
