Combinatorics

Physics

Zero-dimensional space

Topological manifold

Topological index

Topology (electrical circuits)

Pure mathematics

Mathematics

Topological order

Topological vector space

Topological quantum number

Topological space

Symmetry protected topological order

Gene

Topological insulator

Topological entropy in physics

Topological degeneracy

Topological tensor product

Chemistry

Geometry

Theoretical physics

Functional analysis

Quantum mechanics

Homogeneous space

Biochemistry

Quantum

Nature

Using a recently developed formalism called topological quantum chemistry, we perform a high-throughput search of ‘high-quality’ materials (for which the atomic positions and structure have been measured very accurately) in the Inorganic Crystal Structure Database in order to identify new topological phases. We develop codes to compute all characters of all symmetries of 26,938 stoichiometric materials, and find 3,307 topological insulators, 4,078 topological semimetals and no fragile phases. For these 7,385 materials we provide the electronic band structure, including some electronic properties (bandgap and number of electrons), symmetry indicators, and other topological information. Our results show that more than 27 per cent of all materials in nature are topological. We provide an open-source code that checks the topology of any material and allows other researchers to reproduce our results. Topological quantum chemistry and newly developed codes&nbsp;are used to analyse and compute the topological properties of materials in a large crystal database and to identify new topological phases, finding that more than 27 per cent of all materials in nature are topological.

A complete catalogue of high-quality topological materials