Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals
Author(s)
Watanabe, Haruki; Po, Hoi Chun; Vishwanath, Ashvin; Zaletel, Michael
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We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator—a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb–Schultz–Mattis argument invoked spin conservation in an essential way and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches: The first one is an entanglement-based scheme, and the second one studies the system on an appropriate flat “Bieberbach” manifold to obtain the filling conditions for all 230 space groups. These approaches assume only time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.
Date issued
2015-11Department
Massachusetts Institute of Technology. Department of PhysicsJournal
Proceedings of the National Academy of Sciences of the United States of America
Publisher
National Academy of Sciences (U.S.)
Citation
Watanabe, Haruki et al. “Filling Constraints for Spin-Orbit Coupled Insulators in Symmorphic and Nonsymmorphic Crystals.” Proceedings of the National Academy of Sciences 112.47 (2015): 14551–14556. © 2017 National Academy of Sciences
Version: Final published version
ISSN
0027-8424
1091-6490