Quantized electric multipole insulators

TLDR

Topological polarization in crystals is addressed via the Berry phase, but higher multipole moments such as quadrupole and octupole are more challenging, as highlighted by Benalcazar et al. These predictions may be testable in cold‑atom and photonic systems. The authors constructed a theoretical framework to handle higher multipole moments in specific solids. In the presence of certain crystalline symmetries, the quadrupole moment is quantized and the system’s corners host fractionally charged, topologically protected states. Science, p.

Abstract

Corner-dwelling topological states Computing the electric polarization of a crystal is surprisingly tricky, but it can be tackled with the help of a topological concept, the so-called Berry phase. Extensions to higher multiple moments, such as quadrupole and octupole, are even trickier. Benalcazar et al. built a theoretical framework for dealing with these moments in certain types of solids. In the presence of some crystalline symmetries, the quadrupole moment is quantized, and the corners of the system play host to fractionally charged, topologically protected states. These predictions may be testable in cold atom and photonic systems. Science , this issue p. 61