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Twistronics has emerged as a new field where researchers stack atomically thin material layers at specific angles to create electronic behaviors absent in the original ingredients. This approach has already produced superconductivity and fractional Chern insulators, states featuring fractionally charged excitations. A recent international collaboration published two papers in *Science* on September 24 to map these possibilities. The first study analyzed 8,872 entries from computational databases to identify 4,073 materials with nontrivial topology or an obstructed atomic limit. B. Andrei Bernevig of Princeton University explained that every new family of twisted materials offers a chance to ask different questions about quantum matter beyond the few platforms currently known.

The researchers extended topological quantum chemistry to nonmagnetic two-dimensional materials, using symmetries like rotations and reflections to determine how electronic waves fit together. Some patterns possess topology that cannot change without altering the electronic structure. For instance, a quantum spin Hall insulator can be insulating inside while carrying current along its edges protected against disturbances. The team developed crystallographic tables and the Topological 2D Materials Database to distinguish experimentally reported structures from computational candidates, creating a library of building blocks for future research.

The second paper identifies over 1,600 candidates suitable for twisting, including 61 semimetals and 1,568 insulators with simple theoretical descriptions. Led by Yi Jiang, the study found that narrow electronic bands in twisted layers make electron interactions influential, potentially enabling superconductivity or acting as quantum simulators. The catalog includes hexagonal, square, rectangular, and oblique crystal lattices. Leslie M. Schoop of Princeton University noted that some candidates can already be grown into bulk crystals and exfoliated into single layers, providing a practical route from computer simulations to laboratory samples.