Topological Electrides and Quantized Zak Phase

Recent studies on the topology of the band structure in the k-space have revealed possibilities of various topological insulators and topological semimetals. Here, the topological semimetals include the Dirac semimetals, the Weyl semimetals [1,2], and the nodal-line semimetals [1,3]. In my presentation, we show that electrides are suitable for achieving various topological insulating and topological semimetal phases. We present an example of an electride showing the topologically insulating phase characterized by the \pi Zak phase. This can be considered as a limit of the topological nodal-line semimetal [3] like calcium, where the Zak phase is either \pi or 0 depending on the momentum regions divided by the nodal lines. This \pi Zak phase appears as a surface polarization charge, and we propose that this surface charge is useful for carrier doping by using the electride. We also talk about the materials having other topological phases such as a nodal-line semimetal. [1] S. Murakami, M. Hirayama, R. Okugawa, and T. Miyake, Sci. Adv. 3 e1602680 (2017). [2] M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake, Phys. Rev. Lett. 114, 206401 (2015). [3] M. Hirayama, R. Okugawa, T. Miyake, and S. Murakami, Nat. Commun. 8, 14022 (2017).