The topological property of the wave function is closely related to the symmetry of the crystal and electronic states. By combining mathematical physics based on group theory with high-precision first-principles calculations, it is possible to theoretically design topological materials.

We have proposed new materials called topological electrides, which straddle physics and chemistry. Electrides are a group of materials in which electrons e- enter the voids in the crystal and stabilize the structure as anions, and because they have a small work function, they are being studied in the field of catalysis. For example, in the layered insulator (Sc2C)2+2e-, the anion electrons (2e-) spread to interlayer positions, resulting in a unique system with a huge topological polarization due to the anion electrons. Reflecting this topological polarization of the bulk, a topologically protected metallic state appears on the Sc2C surface. Since this surface state originates from the anionic electron, the electron cloud appears floating on the surface. Such topological electronic phases have been found in many electrides, and we have also found that the electride of the well-known mineral apatite corresponds to a higher-order topological phase.

[Phys. Rev. X 8, 031067 (2018). Phys. Rev. Research 2, 043131 (2020).]