  In various topological phases, nontrivial states appear at the boundaries of
the system. In this paper, we investigate anomalous dielectric response caused
by such states caused by the pi Zak phase. First, by using the one-dimensional
Su-Schrieffer-Heeger model, we show that, when the system is insulating and the
Zak phase is pi, the polarization suddenly rises to a large value close to e/2,
by application of an external electric field. The pi Zak phase indicates
existence of half-filled edge states, and we attribute this phenomenon to
charge transfer between the edge states at the two ends of the system. We
extend this idea to two- and three-dimensional insulators with the pi Zak phase
over the Brillouin zone, and find similar anomalous dielectric response. We
also show that diamond and silicon slabs with (111) surfaces have the pi Zak
phase by ab intio calculations, and show that this anomalous response survives
even surface reconstruction involving an odd number of original surface unit
cells. Another material example with an anomalous dielectric response is
polytetrafluoroethylene (PTFE), showing plateaus of polarization at +e by ab
initio calculation, in agreement with our theory.
