Multipole moments and fractional corner charges of insulating materials
How do we characterize and classify the insulating states of matter? Recent advances in the topological approach in condensed-matter physics offer a classification based on the winding and the quantum entanglement in the ground-state wavefunction. Although a nontrivial bulk topology is usually manifested as anomalous surface states, gapless modes are localized to the hinges and corners of the sample in the case of “higher-order” topology.
In this talk, we discuss that even absolutely topologically trivial materials may exhibit fractional charges on their corners and hinges. To predict these boundary signatures from the bulk, we develop a general formulation of bulk multipole moments, directly generalizing the “modern theory” formulation of the bulk polarization. As an example, we discuss e/8 fractional corner charges of grains of “table salt” and propose their direct measurement using atomic force microscopy.
HW and S. Ono, Phys. Rev. B 102, 165120 (2020)
HW and H. C. Po, arXiv:2009.04845.