The well-known ionic crystal NaCl is predicted to have e/8 fractional charge at corners in a cubic sample. The quantization of corner charge may seem unexpected in such a trivial atomic insulator. Being an ionic compound, NaCl is an example of obstructed atomic insulator (OAI), which has mismatched Wannier charge centers and atomic positions. In this talk, I will discuss the emergence of fractional corner charge from the perspective of (i) filling anomaly and (ii) bulk multipole moments. I will introduce the ''real space invariant'', which can be used to diagnose OAIs in practical materials. At last, fractional charges at disclinations will also be mentioned.
. Haruki Watanabe and Hoi Chun Po. Fractional corner charge of sodium chloride. arXiv preprint arXiv:2009.04845, 2020.
. Shang Ren, Ivo Souza, and David Vanderbilt. Quadrupole moments, edge polarizations, and corner charges in the wannier representation. Physical Review B, 103(3):035147, 2021.
. Zhi-Da Song, Luis Elcoro, and B Andrei Bernevig. Twisted bulk-boundary correspondence of fragile topology. Science, 367(6479):794–797, 2020.