Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals
Name
Watanabe-2015-Filling constraints.pdf
Size
710.15 KB
Format
Adobe PDF
Checksum (MD5)
3d804c705f52e355ec32017f37fd6e30
Author(s)
Watanabe, Haruki
Po, Hoi Chun
Vishwanath, Ashvin
Zaletel, Michael
Date Issued
November 2015
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1073/pnas.1514665112
