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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 materials have particular topological arrangements in the geometry of their electronic band structures, resulting in robust surface states and unconventional electromagnetic activity. But how many topological materials exist, their identity and their abundance is unclear. The remarkable field of topological insulators and semimetals has combined deep theoretical insights with almost immediate material predictions and their experimental discovery. Since the field began 13 years ago1-3, the prevalent impression in the physics and chemistry communities has been that topological materials represent an infinitesimal proportion of the total number of materials existing in nature. Even though it has led to a comparatively large number of successes, the method of predicting new topological classes and corresponding materials has so far been based mostly on educated guesses. In this way, time-reversal2,3, mirror-symmetric and nonsymmorphic topological insulators4,5; Dirac6,7, Weyl8-11 and nodal-chain12 semimetals; new fermions13 and many other states in realistic materials have been predicted. However, the deficiencies of the method are clear: only about 20 topological semimetals have been predicted and experimentally discovered so far. The problem underlying the efficient discovery of materials has been a missing link between the chemistry of different compounds and their topological properties.
In topological quantum chemistry (TQC)14, a link has been established between the topology of a nonmagnetic material and its crystal symmetry, position and content of the orbitals. The basis of the approach is elementary band representations (EBRs)15,16, which represent all of the 10,398 (with/without time reversal: 4,757/5,641) building blocks of bands that...