Electric polarization as a bulk quantity and its relation to surface charge

A definition of the electric polarization of an insulating crystalline solid is given in terms of the centers of charge of the Wannier functions of the occupied bands. The change of this quantity under an adiabatic evolution of the Hamiltonian has previously been shown to correspond to the physical change in polarization. Here, we show that the polarization as defined above also has a direct and predictive relationship to the surface charge which accumulates at an insulating surface or interface.