  The Born effective charge, Z*, that describes the polarization created by
collective atomic displacements, can be computed from first-principles by
different techniques. Its band-by-band decomposition appeared recently as a
powerful tool for the microscopic characterisation of the bonding in solids. We
describe the connections between the different expressions used for the
computation of Z*, and analyze the possible associated 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 an interesting
physical meaning.
