Each new family of twisted materials has repeatedly brought new rules for how electrons move and interact. In the language of theorists, each family offers a different Hamiltonian, the mathematical object that specifies a system’s energies and interactions, and therefore a new kind of quantum simulator. A recent Nature study of so-called M-point twisting illustrated the principle vividly: by changing the starting electronic structure of the constituent layers, researchers accessed fundamentally different models with new symmetries. The implication is that exploring other atomic architectures could uncover quantum states and theoretical models that today’s familiar platforms, built almost entirely around graphene and dichalcogenides, simply cannot reach.

Now an international collaboration spanning more than a dozen institutions has provided both the raw building blocks and a practical guide to that vast search. In two back-to-back papers publishing in Science on September 24, the team presents a sweeping computational survey of the two-dimensional materials universe. The first paper maps the electronic structures and topology of nearly 9,000 two-dimensional entries, regardless of whether they are topological. The second paper identifies more than 1,600 candidates whose electronic properties make them promising for twisting, each offering a different starting point for constructing entirely new kinds of quantum simulators.

The motivation behind the effort is straightforward but profound. Every new family of twisted materials gives researchers a chance to ask a different question about quantum matter, and the field has so far sampled only a handful of the possibilities. B. Andrei Bernevig, a professor of physics at Princeton University and coauthor of both studies, framed the ambition directly: the goal is to move beyond the few platforms currently known and explore the enormous range of physics that other layers and other twist angles could make possible. The two catalogs are designed to turn that open-ended dream into a systematic research program that any laboratory with an internet connection can join.

The first study extends topological quantum chemistry, a theoretical framework that connects a crystal’s chemistry and symmetries to the topology of its electronic states, to nonmagnetic two-dimensional materials. Symmetries are the operations, such as rotations and reflections, that leave a crystal’s atomic pattern unchanged, and they constrain how electronic waves can fit together throughout the crystal. Some electronic patterns carry a special robustness: their topology cannot change without a fundamental alteration of the electronic structure. A quantum spin Hall insulator, for example, can be insulating in its interior while carrying current along its edges through channels protected against certain disturbances. Such states offer a route to studying robust quantum behavior and have motivated a wide range of proposals for new electronic devices.

Working from entries in two computational materials databases, the researchers analyzed 8,872 two-dimensional materials and identified 4,073 with nontrivial topology or an obstructed atomic limit. The latter describes a different kind of unusual electronic organization: in one such class, symmetry constrains the centers of electronic charge to sit away from the atoms themselves. Cutting such a crystal along particular boundaries can then expose distinctive electronic states localized at the surface. Luis Elcoro of the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, senior author of one of the studies, explained the philosophy behind the work: the symmetry of a crystal yields rules for how electronic states can be arranged, and the team developed those rules for atomically thin layers and turned them into tools that other researchers can apply across thousands of materials.

Alongside the calculations, the collaboration developed crystallographic tables, analysis programs and a public resource called the Topological 2D Materials Database, which carefully distinguishes experimentally reported structures from purely computational candidates. Crucially, the catalog records electronic band structures, the spectrum of energies available to electrons, for layers both with and without topology. Its nearly 9,000 entries thus form a library of Lego-like building blocks. Two identical layers can be combined into a homobilayer, while two different layers can form a heterobilayer, and adding the freedom to choose their relative twist angle multiplies the possibilities into what the authors describe as an embarrassment of riches. It is precisely this combinatorial explosion that the second paper brings structure to.

The second study is built on the physics of moiré patterns, the large-scale interference patterns that emerge when two fine meshes are overlaid with a slight rotation. Something analogous happens when two atomically thin crystals are stacked and twisted: a moiré superlattice forms that dramatically changes how electrons move through the combined system. In suitable materials, twisting produces narrow electronic bands, in which electrons’ kinetic energy is suppressed and interactions between electrons become especially influential. This regime is fertile ground for superconductivity, magnetism and fractional quantum states, and it offers a controllable way to build quantum simulators, materials that physically enact models of interacting electrons, including models whose behavior remains unknown even to theorists.

Led by Yi Jiang, a Princeton postdoctoral researcher, the second study identifies 61 semimetal candidates and 1,568 insulating candidates whose electronic structures are suited to twisting and admit relatively simple theoretical descriptions. The candidates span hexagonal, square, rectangular and oblique crystal lattices, as well as different patterns of electron motion, so that each starting geometry corresponds to a different physical problem. Twisted square lattices, for instance, could simulate the Hubbard model, the paradigmatic framework central to research on high-temperature superconductivity, while rectangular systems could reveal behavior resembling electrons confined to one-dimensional chains. The team’s earlier M-point twisting study, published in Nature in 2025, showed that a different starting electronic structure produces models with new symmetries and new possibilities for simulating interacting electrons, and the new catalog vastly expands the range of such starting points.

The work also reaches beyond computation into the laboratory. The researchers calculated selected twisted bilayers and found narrow bands in compounds including tin diselenide and hafnium disulfide, and they grew bulk crystals of these compounds along with tin disulfide, gallium telluride and zirconium nitride chloride. Initial sample preparation confirmed that the grown materials can be exfoliated, peeled down layer by layer, to single atomic sheets, a critical practical requirement for assembling twisted devices. Leslie M. Schoop, professor of chemistry and director of the Princeton Center for Complex Materials, emphasized that connecting the catalog to crystal growth and exfoliation provides a practical route from an electronic structure computed on a computer to a real sample in the laboratory. Kin Fai Mak of Cornell University added that some candidates are already crystals that can be grown and peeled to a single layer, giving experiments a concrete starting point for building new twisted structures and testing the physics predicted for them. The catalog classifies candidates purely by their electronic suitability for twisting, so the next step is to assemble the layers into devices and probe their collective behavior, a challenge that coauthor Dmitri K. Efetov of Ludwig Maximilian University of Munich says will involve controlling both twist angle and electron density in each new material.

The shared database, assembled by Princeton physics researcher Nicolas Regnault, who is also affiliated with the Flatiron Institute, the École normale supérieure in Paris and the French National Centre for Scientific Research, is intended as a community resource that lets researchers compare individual layers and select candidates for whichever physics they wish to investigate. The logic of the project is deliberately bidirectional: theorists can start from a known problem about interacting electrons and ask which crystal, which layers and which twist will let them study it, while experiments on the cataloged materials may reveal collective states no one anticipated. As Bernevig concluded, the exciting part is that an experiment can also show researchers something they did not know to ask. The publicly available preprints behind the studies, covering the two-dimensional topological quantum chemistry catalog and the theoretically twistable material database, ensure that the full library of building blocks, from quantum spin Hall insulators to Hubbard-model-ready square lattices, is now open to anyone hunting for the next quantum state of matter.

Subject of Research: Computational catalogs of topological and twistable two-dimensional materials for quantum simulation

Article Title: New catalogs map the quantum possibilities of atomically thin materials

Article References: New catalogs map the quantum possibilities of atomically thin materials. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: twistronics, two-dimensional materials, topological quantum chemistry, moiré patterns, quantum simulators, superconductivity, quantum spin Hall insulators, twisted bilayers, materials database, fractional Chern insulators, crystal growth, narrow bands