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

TL;DR

This paper establishes strict filling constraints for band insulators across all 230 space groups, revealing conditions that enforce gapless electronic structures due to nonsymmorphic symmetries, with implications for topological materials.

Contribution

It provides the first comprehensive, rigorous bounds on electron fillings compatible with band insulators for all space groups, surpassing previous results for interacting systems.

Findings

Tight bounds on electron fillings for band insulators across all space groups.

Explicit models constructed for all allowed fillings.

Identification of filling constraints that enforce gapless band structures.

Abstract

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.