Unconventional superconductivity and other intriguing correlated states appear more often in a material that has many electrons at the Fermi level, that is, the energy level of the highest occupied states. These electrons are responsible for most of the electrical and optical behavior of a material. And the more of them there are, the more likely they are to interact with each other as they move through the material.
A material with many electronic states at the same energy usually has what is called a flat band, referring to a plateau in the band structure. The emergence of a flat band explains superconductivity in twisted bilayer graphene (see physics todayJanuary 2020, page 18), among other phenomena.
Although the flat bands of graphene systems are man-made, some crystals have them naturally. The trick is figuring out which materials. Today, B. Andrei Bernevig (International Physics Center of Ikerbasque and Donostia in Spain and Princeton University), Nicolas Regnault (Ecole Normale Supérieure in France and Princeton University) and their colleagues carried out extensive computational research on the flat band materials. The results, available in their open database, can guide future studies.
Previously, many of the same researchers created the Topological Materials Database, which includes information such as lattice structures, density of states, and simplification. ab-initio band structures of 55,206 crystals. In the new study, the researchers performed an automated search of this database to find promising indicators of correlated behavior. For simplicity, they limited their search to three-dimensional paramagnetic materials, but the same strategy should apply to two-dimensional and magnetic materials.
Bernevig and his colleagues evaluated the band structure of each material for the number of flat segments, the amount of band structure covered by each segment, and its degree of flatness, i.e. low energy variation from one state to another. Some flat bands are more likely than others to create interesting electronic properties. In a material with distant atoms, for example, conduction electrons may be stuck at distant atomic sites and therefore unable to interact in any meaningful way, despite the presence of short flat bands. A material with spread electronic wave functions, usually due to topological effects, avoids this problem.
To filter out uninteresting flat bands, the researchers excluded materials that did not have a large sharp peak in the density of states near the Fermi level. They also searched for crystal structures known to host extended electronic wavefunctions, such as kagome lattices (see physics todayFebruary 2007, page 16).
In the end, the researchers compiled a list of 2,379 materials with high-quality flat bands, 345 of which are particularly strong candidates for correlated behavior. Theorists and experimentalists looking for a materials system worthy of further research can now check the website for leads. (N. Regnault et al., Nature 603824, 2022.)