Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups

Haruki Watanabe, Hoi Chun Po, Michael P. Zaletel, Ashvin Vishwanath

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


Nonsymmorphic symmetries like screws and glides produce electron band touchings, obstructing the formation of a band insulator and leading, instead, to metals or nodal semimetals even when the number of electrons in the unit cell is an even integer. Here, we calculate the electron fillings compatible with being a band insulator for all 230 space groups, for noninteracting electrons with time-reversal symmetry. Our bounds are tight - that is, we can rigorously eliminate band insulators at any forbidden filling and produce explicit models for all allowed fillings - and stronger than those recently established for interacting systems. These results provide simple criteria that should help guide the search for topological semimetals and, also, have implications for both the nature and stability of the resulting nodal Fermi surfaces.

Original languageEnglish (US)
Article number096404
JournalPhysical review letters
Issue number9
StatePublished - Aug 24 2016

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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