Band-by-band decomposition of the Born effective charges

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.