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.

Topological polarization, dual invariants, and surface flat bands in crystalline insulators

“…This symmetry is not necessary for the stability of the nodal lines [41,63], but in its absence the surface states become "drumhead" states with some dispersion. The same is expected for the approximately flat bands of the crystalline insulator [17].…”

“…We explicitly verified that the response of the polarization to the properly defined deformations is quantized, see Eq. (17), and that the corresponding surface flat band is present throughout the whole BZ. This is distinct from the nodal line semimetals, where there is also a flat band, but where this flat band occupies only part of the surface BZ.…”

“…From the comparison of the polarization to the Zak phase, see, e.g., Refs. [13,17,18] for insulators and superconductors and Refs. [38,39] for gapless systems, we conclude that in some cases the invariants N a can be written simply in terms of an effective Hamiltonian H (p) = 1/G(p, ω = 0), which is the inverse of the Green's function at zero frequency.…”

“…In noninteracting PT -symmetric insulators [17] and superconductors [18] these invariants determine the Berry phase change along the loop (the Zak phase), which is 2π N a . In nodal line semimetals the nonzero Zak phase produces zero-energy surface states, which form a flat band [38,39].…”

“…It has been discussed, e.g., in Refs. [5][6][7][8][9][10], and has recently attracted renewed interest [11][12][13][14][15][16][17][18][19]. In 3D, the response is defined by the polarization charge density that scales like 1/[ 2 ].…”