Journal
NATURE PHYSICS
Volume 9, Issue 5, Pages 299-303Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/NPHYS2600
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Funding
- Simons Foundation
- National Science Foundation at the Aspen Center for Physics through the Frustrated Magnets programme at the Kavli Institute for Theoretical Physics [1066293, PHY11-25915, DMR-1007028, DMR-1206728]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206728] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1007028] Funding Source: National Science Foundation
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Band insulators appear in a crystalline system only when the filling-the number of electrons per unit cell and spin projection-is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott insulator; that is, it is either gapless or, if gapped, exhibits fractionalized excitations and topological order. We raise the inverse question-at an integer filling is a band insulator always possible? Here we show that lattice symmetries may forbid a band insulator even at certain integer fillings, if the crystal is non-symmorphic-a property shared by most three-dimensional crystal structures. In these cases, one may infer the existence of topological order if the ground state is gapped and fully symmetric. This is demonstrated using a non-perturbative flux-threading argument, which has immediate applications to quantum spin systems and bosonic insulators in addition to electronic band structures in the absence of spin-orbit interactions.
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