  The Born effective charge, Z*, that describes the polarization created by
collective atomic displacements, can be computed from first-principles
following different techniques. We establish the connections existing between
these different formulations, and analyze the related band-by-band
decompositions. We show that unlike for the full Z*, the different band-by-band
values are not equal, and emphasize that one of them has a natural physical
meaning in terms of Wannier functions.
