2012/12/10 by S. A. Parameswaran, Ari M. Turner, Daniel P. Arovas +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1038/nphys2600
published as Nature Physics 9, 299 (2013) · 5 pages, 3 figures, 1 table in the main text + 4 pages supplementary material. v2 with typos corrected and updated figures and references
arxiv created 2012/12/10 · arxiv updated 2013/05/07
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.