  We discuss the change of the corner charge for noninteracting two dimensional
insulators with inversion symmetry undergoing adiabatic evolution. We show that
the change of the corner charge is accounted for by the adiabatic current
flowing along the edges of the system. The study of systems with quasi-1D
geometry is necessary to derive the analytical expression for the adiabatic
current. This fact suggests that the change of the corner charge is neither a
purely bulk nor edge effect, but rather a mixed one. The derived adiabatic
current was examined and shows good agreement with the numerical calculation of
Benalcazar-Bernevig-Hughes model.
