Catalogue of Flat Band Stoichiometric Materials*

Topological electronic flatten bands near or at the Fermi level are a promising avenue towards un-conventional superconductivity and correlated insulating states. In this work, we present a catalogueof all the three-dimensional stoichiometric materials with flat bands around the Fermi level that ex-ist in nature. We consider 55,206 materials from the Inorganic Crystal Structure Database (ICSD)catalogued using the Topological Quantum Chemistry website which provides their structural pa-rameters, space group (SG), band structure, density of states and topological characterization. Weidentify several signatures and properties of band flatness: bandwidth, peaks in the density of states,band topology, range of momenta over which the band is flat and the energy window around theFermi level where the flat bands is situated. Moreover, we perform a high-throughput analysis of allcrystal structures to identify those hosting line-graph or bipartite sublattices - either in two or threedimensions - that likely lead to flat bands. From this trove of information, we create the MaterialsFlatband Database website, a powerful search engine for future theoretical and experimental studies.We use it to manually extract a curated list of 2,379 materials potentially hosting flat bands whosecharge centers are not strongly localized on the atomic sites, out of which we present in minute de-tails the 345 most promising ones. In addition, we showcase five representative materials (KAg[CN]2in SG 163 (P -31c), Pb2Sb2O7in SG 227 (Fd -3m), Rb2CaH4in SG 139 (I4/mmm), Ca2NCl in SG166 (R -3m) and WO3in SG 221 (Pm -3m)) and provide a theoretical explanation for the origin of their flat bands that close to the Fermi energy using the S-matrix method.