  Modern polarization theory yields surface bound charge associated with
spontaneous polarization of bulk. However, understanding polarization in nano
systems also requires a proper treatment of charge transfer between surface
dangling bonds. Here, we develop a real-space approach for total polarization
and apply it to wurtzite semiconductors and BaTiO3 perovskite. First-principles
calculations utilizing this approach not only yield spontaneous bulk
polarization in agreement with Berry phase calculations, but also uncover
phenomena specific to nano systems. As an example, we show surface passivation
leads to a complete quenching of the piezoelectric effect, which reemerges only
at larger length scale and/or spontaneous polarization.
