Abstract
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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Acknowledgements
We thank I. Kimchi and D. Stamper-Kurn for collaboration on related work, R. Roy for many detailed conversations, M. Hermele, M. Oshikawa, S. Coh and M. Zaletel for stimulating discussions and M. Norman for valuable comments on the manuscript. This work is supported by the Simons Foundation (S.A.P. and A.V.) and by the National Science Foundation Grants No. 1066293 at the Aspen Center for Physics (S.A.P., D.P.A., A.V.), PHY11-25915 through the Frustrated Magnets programme at the Kavli Institute for Theoretical Physics (S.A.P., A.V.), DMR-1007028 (D.P.A.) and DMR-1206728 (A.V.).
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Parameswaran, S., Turner, A., Arovas, D. et al. Topological order and absence of band insulators at integer filling in non-symmorphic crystals. Nature Phys 9, 299–303 (2013). https://doi.org/10.1038/nphys2600
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DOI: https://doi.org/10.1038/nphys2600
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