Filling-enforced obstructed atomic insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no ab initio calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples.

Figure 1

Topological classification of the gapped bands satisfying compatibility relations. High-throughput searches of topological bands, including strong topological bands and fragile bands, are partially done. Topologically trivial bands can be classified into obstructed atomic limit bands and trivial atomic bands. Although a full topological classification of obstructed bands has not been achieved, we perform high-throughput search of filling enforced obstructed bands in the present work.

Figure 2

FeOAI in 1-$d$. (a) A 1-$d$ atomic chain with a Wyckoff position $2i$ occupied by atoms. (b) Schematic diagram of the band structure of the 1-$d$ model in (a). The blue and red bands are valence and conduction bands, respectively.