Anomalous dielectric response in insulators with a topological π Zak phase

In the topological phase of the Su-Schrieffer-Heeger model, the Zak phase is equal to π. While it corresponds to the e/2 polarization, there is no electric dipole moment because of inversion symmetry. We find that an external electric field gives rise to an abrupt rise of the dipole moment, close to e/2. This sudden uprise of the dipole moment is attributed to the midgap state at the two ends of the system. We also extend this idea to two- and three-dimensional insulators with the π Zak phase over the whole Brillouin zone, and show that similar sudden uprise of the polarization by an externa electric field happens also in these cases, if the midgap boundary states due to the π Zak phase has sufficiently flat dispersions. Finally, we discuss possible candidate materials for this behavior, including the (111) surface of Si and the (111) surface of a topological electride Sc₂C.