Topological order and absence of band insulators at integer filling in non-symmorphic crystals

By S. Parameswaran, Ari M. Turner, D. Arovas, Ashvin Vishwanath. Nature Physics, 2012

149 citations recorded by the source corpus.

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. A crystal is a band insulator if the energy bands are filled with electrons. Partially filled bands result in a metal, or sometimes a Mott insulator when interactions are strong. A study now shows that for many crystalline structures, the Mott insulator is the only possible insulating state, even for filled bands.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/988bce9b8c94507be8b2d399e104d39c31b4fb37

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Citations in the corpus

Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, background): “[16] Siddharth A Parameswaran, Ari M Turner, Daniel P Arovas, and Ashvin Vishwanath, “Topological order and absence of band insulators at integer filling in nonsymmorphic crystals,” Nat.”
Weyl and Dirac semimetals in three-dimensional solids (2017, background): “This presents an example of a “filling enforced semimetal” (Parameswaran, 2015; Parameswaran et al., 2013; Watanabe et al., 2015) where the zone boundary degeneracy requires that electron count for a filled band actually results in a gapless state where the conduction and valence bands contact each…”