[Paper Review] Filling-Enforced Obstructed Atomic Insulators

Yuanfeng Xu, Luis Elcoro+7 more|arXiv (Cornell University)|Jun 17, 2021

History and advancements in chemistry21 citations

TL;DR

This paper introduces filling-enforced obstructed atomic insulators (feOAIs), a class of topologically trivial insulators whose obstructed nature is determined solely by electron count and Wyckoff positions, without requiring ab-initio calculations. The authors derive necessary and sufficient conditions for feOAIs in all 1651 Shubnikov space groups and perform a high-throughput search identifying 638 unique materials as paramagnetic feOAIs, with 475 exhibiting indirect band gaps and metallic surface states due to a non-localized center of charge.

ABSTRACT

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.

Motivation & Objective

• To identify a subset of topologically trivial insulators that are obstructed atomic insulators (OAIs) based solely on electron count and Wyckoff positions.
• To derive necessary and sufficient conditions for a topologically trivial insulator to be a filling-enforced OAI (feOAI) in all 1651 Shubnikov space groups.
• To enable high-throughput identification of feOAIs without ab-initio band structure calculations, using only symmetry and electron counting.
• To demonstrate the existence of metallic obstructed surface states in feOAIs through material examples.

Proposed method

• The authors use topological quantum chemistry (TQC) to classify band structures via symmetry data vectors and their decomposition into elementary band representations (EBRs).
• They define feOAIs as insulators where the electron count and occupied Wyckoff positions enforce a non-trivial band structure that cannot be represented as a sum of atomic orbitals on occupied sites.
• The method relies on identifying when the symmetry data vector of a band structure cannot be expressed as a non-negative integer combination of EBRs induced from occupied Wyckoff positions, indicating an obstructed Wannier charge center (OWCC).
• The authors derive filling-enforcement conditions for each of the 1651 Shubnikov space groups, specifying electron counts (Ne) that enforce the OAI state.
• They perform a high-throughput search using the Topological Quantum Chemistry database, filtering materials by electron count and Wyckoff site occupancy to identify feOAIs.
• Metallic surface states are analyzed via band structure calculations for representative feOAI examples, confirming the presence of obstructed surface states.

Experimental results

Research questions

• RQ1 Can a topologically trivial insulator be identified as an obstructed atomic insulator (OAI) without ab-initio band structure calculations, based only on electron count and Wyckoff positions?
• RQ2 What are the necessary and sufficient conditions for a topologically trivial insulator to be a filling-enforced OAI (feOAI) in all 1651 Shubnikov space groups?
• RQ3 How many materials in the ICSD database are predicted to be paramagnetic feOAIs, and what fraction have indirect band gaps?
• RQ4 Do feOAIs exhibit metallic surface states due to a non-localized center of charge, and can this be confirmed through band structure calculations?

Key findings

• The authors identify 957 ICSD entries (638 unique materials) as paramagnetic filling-enforced obstructed atomic insulators (feOAIs), with 738 (475 unique) materials having an indirect band gap.
• The feOAI condition is determined solely by electron count (Ne) and Wyckoff position occupancy, enabling identification without ab-initio calculations.
• Among the 638 unique feOAI materials, 475 have indirect band gaps, indicating that the obstructed nature persists in a significant fraction of the candidates.
• The metallic obstructed surface states in feOAIs are confirmed through band structure calculations, demonstrating a center of charge not localized on atomic sites.
• The study provides a complete set of filling-enforcement conditions for all 1651 Shubnikov space groups, enabling systematic classification of feOAIs.
• The results show that feOAIs are a distinct class of topologically trivial insulators with non-trivial electronic response due to a center of charge located at an unoccupied Wyckoff position.