Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals

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, i.e. it is either gapless or, if gapped, displays 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 a majority of 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.

5 pages, 3 figures, 1 table in the main text + 4 pages supplementary material. v2 with typos corrected and updated figures and references

References in corpus (4)

• Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Insulator, conductor and commensurability: a topological approach
• Space group symmetries and low lying excitations of many-body systems at integer fillings

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