Quantum mechanics

Fermi level

Cosmology

Materials science

Theoretical computer science

Bipartite graph

Computer science

Band gap

Physics

Organic chemistry

Stoichiometry

Graph

Mathematics

Flatness (cosmology)

Condensed matter physics

Combinatorics

Chemistry

Electron

Topology (electrical circuits)

Nature

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1-3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

Catalogue of flat-band stoichiometric materials