Anomalous dielectric response in insulators with the π Zak phase

Abstract

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 π 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 π, the polarization suddenly rises to a large value close to e/2, by application of an external electric field. The π Zak phase indicates the 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 π 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 π Zak phase by ab initio 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.