The (High Quality) Topological Materials In The World (1807.10271v3)

Abstract: "Topological Quantum Chemistry (TQC) links the chemical and symmetry structure of a given material with its topological properties. This field tabulates the data of the 10398 real-space atomic limits of materials, and solves the compatibility relations of electronic bands in momentum space. A material that is not an atomic limit or whose bands do not satisfy the compatibility relations, is a topological insulator/semimetal. We use TQC to find the topological stoichiometric non-magnetic, "high-quality'' materials in the world. We develop several code additions to VASP which can compute all characters of all symmetries at all high-symmetry points in the Brillouin Zone (BZ). Using TQC we then develop codes to check which materials in ICSD are topological. Out of 26938 stoichiometric materials in our filtered ICSD database, we find 2861 topological insulators (TI) and 2936 topological semimetals (2505 and 2560 non-f electron, respectively). Our method is uniquely capable to show that none of the TI's found exhibit fragile topology. We partition the topological materials in different physical classes. For the majority of the 5797 "high-quality'' topological material, we compute: the topological class (equivalence classes of TQC elementary band representations -- equivalent to the topological index), the symmetry(ies) that protects the topological class, the representations at high symmetry points and the direct gap (for insulators), and the topological index. For topological semimetals we then compute whether the system becomes a topological insulator (whose index/class we compute) upon breaking symmetries -- useful for experiments. 2152 more TI's are obtained in this way. For almost all 5065 non-f-electron topological materials, we provide the electronic band structures, allowing the identification of quantitative properties (gaps, velocities). Remarkably, our exhaustive results show that a large proportion ( ~ 24% !) of all materials in nature are topological (confirmed by calculations of "low-quality'' materials). We confirm the topology of several new materials by Wilson loop calculations. We added an open-source code and end-user button on the Bilbao Crystallographic Server (BCS) which checks the topology of any material. We comment on the chemistry of each compound and sample part of the "low-quality'' ICSD data to find more materials."

• The paper introduces a robust TQC framework to classify over 26,000 compounds, pinpointing 3,307 topological insulators and 4,078 semimetals.
• The study combines high-throughput computations with symmetry analysis to accurately verify band connectivity and delineate topological phases.
• The research offers an open-source catalogue that empowers experimentalists to reproduce findings and explore new topological materials.

Overview of "A Complete Catalogue of High-Quality Topological Materials"

The paper "A Complete Catalogue of High-Quality Topological Materials" presents a comprehensive paper that significantly advances the field of topological materials by categorizing a broad array of these materials based on their crystalline symmetries and electronic structures. Utilizing an innovative theoretical framework called Topological Quantum Chemistry (TQC), the authors systematically analyze and classify topological insulators and semimetals in nature. Their methodology blends high-throughput computations with detailed symmetry analyses, resulting in significant insights into the prevalence and characteristics of topological phases in crystalline solids.

Methodology and Results

The authors leverage the Inorganic Crystal Structure Database (ICSD), examining 184,270 materials and refining the set to 26,938 stoichiometric compounds. They exclude materials with unreliable data, alloys, and f-electron complications to distill a high-quality dataset. Through their approach, they identify 3,307 topological insulators and 4,078 topological semimetals. An intriguing revelation is the absence of fragile topological phases among the materials studied.

Key to their analysis is the use of TQC, which efficiently links the topological property of materials with their crystal symmetries. By employing established program tools such as BANDREP and DCOMPREL from the Bilbao Crystallographic Server, the authors computationally verify the connectivity of bands and categorize materials based on whether their band structures conform to elementary band representations (EBRs). If a material's valence bands cannot be represented as a linear combination of EBRs, using both positive and negative coefficients, it is declared topologically non-trivial.

Classification and Implications

The results are stratified into strong and weak topological phases and further broken down into physical classes such as enforced semimetals (ES/ESFD), split EBRs (SEBR), and no-linear combination (NLC) insulators. Additionally, the authors introduce an index system (TQC numbering) for systematic tracking and reference, underscoring the ease of data reproducibility and cross-verification.

From a practical standpoint, this catalog serves as a vital resource for experimentalists seeking candidate materials for fabrication and testing. The open-source accessibility of their code on the Bilbao Crystallographic Server amplifies the utility of their work. It facilitates the replication of their results and the identification of topological properties in other materials by the broader research community.

Theoretical and Future Directions

Theoretically, this research consolidates topological classifications by offering a robust approach grounded in crystallographic data. It marks a transition from heuristic predictions to formalized computational methodologies, reducing ambiguity in identifying topological materials. This comprehensive catalog provides a benchmark for the coexistence and interaction of topological phases within a material system.

Future avenues hinted at by this work involve extending analyses to the remaining ICSD database, potentially uncovering additional topological materials. Furthermore, enhanced computational techniques, such as dynamical mean-field theory, are proposed for a more accurate characterization of complex materials, particularly those involving strong electron correlations like d/f-electron systems.

This paper sets the stage for continuous discovery and finer classification of topological phases, promising significant advancements in material design with technological implications spanning electronic, optical, and quantum computing applications. The authors effectively argue that through systematic and reproducible methodologies, the understanding and utilization of topological materials can transition from theory to practical application, heralding a new phase in material science exploration.