Database identifies materials likely to host correlated states

Unconventional superconductivity and other intriguing correlated states show up more often in a material that has many electrons at the Fermi level — that is, the energy level of the highest occupied states. Those electrons are responsible for most of a material’s electrical and optical behaviors. And the more of them there are, the more likely they are to interact with each other as they move around the material.

A material with many electronic states at the same energy typically has what’s known as a flat band, in reference to a plateau in the band structure. The emergence of a flat band explains the superconductivity in twisted bilayer graphene (see Physics TodayJanuary 2020, page 18), among other phenomena.

Although the flat bands in graphene systems are contrived, some crystals happen to have naturally occurring ones. The trick is figuring out which materials. Now B. Andrei Bernevig (Ikerbasque and Donostia International Physics Center in Spain and Princeton University), Nicolas Regnault (the École Normale Supérieure in France and Princeton University), and their colleagues have done an extensive computational search for flat-band materials. The results, available in their open database, can guide future studies.

The crystal structure of KAg (CN)2which hosts an
approximate kagome sublattice. Credit: N. Regnault et al., Nature 603824, (2022)

Previously, many of the same researchers created the Topological Materials Database, which includes such information as the lattice structures, density of states, and simplified ab initio band structures of 55 206 crystals. In the new study, the researchers ran an automated search through that database for promising indicators of correlated behavior. For simplicity, they restricted their search to three-dimensional paramagnetic materials, but the same strategy should apply to two-dimensional and magnetic ones.

Bernevig and his colleagues evaluated each material’s band structure for the number of flat segments, how much of the band structure each segment covers, and how flat it is — that is, how little the energy varies from state to state. Some flat bands are more likely than others to create interesting electronic properties. In a material with far-apart atoms, for example, the conduction electrons can be stuck at distant atomic sites and thus unable to significantly interact, despite the presence of short flat bands. A material with spread-out electron wavefunctions, usually as a result of topological effects, avoids that issue.

To filter uninteresting flat bands, the researchers excluded materials that do not have a large sharp peak in the density of states near the Fermi level. They also searched for crystal structures known frequently to host extended electron wavefunctions, such as kagome lattices (see Physics TodayFebruary 2007, page 16).

In the end, the researchers compiled a list of 2379 materials with high-quality flat bands, 345 of which are especially strong candidates for correlated behavior. Theorists and experimentalists in search of a materials system worthy of further research can now consult the website for leads. (N. Regnault et al., Nature 603824, 2022.)

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