Researchers at the University of Illinois at Urbana-Champaign and Princeton University have theoretically predicted a new class of insulating phases of matter in crystalline materials, pinpointed where they might be found in nature, and in the process generalized the fundamental quantum theory of Berry phases in solid state systems. What’s more, these insulators generate electric quadrupole or octupole moments—which can be thought of roughly as very specific electric fields—that are quantized. Quantized observables are a gold standard in condensed matter research, because experimental results that measure these observables have to, in principle, exactly match theoretical predictions—leaving no wiggle room for doubt, even in highly complex systems.