Twistronics has become a new alchemy of materials. By choosing atomically thin layers, stacking them and changing their relative angle, researchers can create electronic behavior absent from the original ingredients. Twisted graphene and transition metal dichalcogenides have already yielded superconductivity and fractional Chern insulators, states with fractionally charged excitations. One of physics’ most active frontiers now has a moonshot ambition: to design entirely new forms of quantum matter.
New families of twisted materials have repeatedly brought new rules for how electrons move and interact—a different Hamiltonian—and new kinds of quantum simulators. The team’s recent Nature study of M-point twisting illustrates how changing the starting electronic structure opens different physics. Exploring other atomic architectures could therefore uncover quantum states and models that today’s familiar platforms cannot reach.
Now, in two back-to-back papers publishing in Science on September 24, an international collaboration provides both the building blocks and a guide to that vast search . The first maps the electronic structures and topology of nearly 9,000 two-dimensional entries , whether topological or not. The second identifies more than 1,600 candidates for twisting, with different electronic starting points that could enable entirely new kinds of quantum simulators .
“Every new family of twisted materials gives us a chance to ask a different question about quantum matter. We want to move beyond the few platforms we know and explore the enormous range of physics that other layers and other twists could make possible,” said B. Andrei Bernevig, a Princeton professor of physics and coauthor of both studies.
The first study extends topological quantum chemistry, a theory connecting 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. They help researchers determine how electronic waves can fit together throughout the crystal.
Some patterns have a special property: their topology cannot change without a fundamental alteration of the electronic structure. A quantum spin Hall insulator, for example, can be insulating inside 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 proposals for new electronic devices.
The researchers analyzed 8,872 entries from two computational materials databases 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 lie away from the atoms. Cutting the crystal at particular boundaries can then expose distinctive electronic states.
“The symmetry of a crystal gives us rules for how its electronic states can be arranged. We developed those rules for layers and turned them into tools that researchers can apply to thousands of materials,” said Luis Elcoro of the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, and senior author of one of the studies.
Alongside the calculations, the team developed crystallographic tables, analysis programs and the Topological 2D Materials Database, distinguishing experimentally reported structures from computational candidates.
Crucially, the catalog records electronic band structures—the energies available to electrons—for layers with and without topology. Its nearly 9,000 entries form a library of Lego-like building blocks. Two identical layers can make a homobilayer; two different layers can make a heterobilayer. Add the freedom to choose their relative angle, and the possibilities multiply into an embarrassment of riches. The second paper brings structure to this enormous search.
“The first catalog gives us the electronic building blocks. We can then ask which ones to combine and twist,” said Urko Petralanda of the University of the Basque Country and a first author of one study.
Lay two fine meshes over one another and turn one slightly: a larger pattern appears. Something similar happens when two atomically thin crystals are stacked and twisted, creating a moiré pattern that changes how their electrons move.
In suitable materials, twisting produces narrow electronic bands, making interactions between electrons especially influential. This is fertile ground for superconductivity, magnetism and fractional quantum states. It also offers a way to build quantum simulators: controllable materials that enact models of interacting electrons, including models whose behavior is still unknown.
Led by Yi Jiang and colleagues, the second study identifies 61 semimetal candidates and 1,568 insulating candidates with electronic structures suited to twisting and relatively simple theoretical descriptions.
“We looked for layers whose electronic structure is simple enough that we can understand what twisting is likely to do. Choosing a different crystal pattern or a different kind of electronic state gives us access to a different physical problem,”explained Yi Jiang, Princeton postdoctoral researcher and lead author of the second study.
The candidates span hexagonal, square, rectangular and oblique crystal lattices, as well as different patterns of electron motion. Twisted square lattices could simulate the Hubbard model, central to research on high-temperature superconductivity. Rectangular systems could reveal behavior resembling electrons moving along one-dimensional chains.
The group’s M-point twisting study, published in Nature in 2025, illustrates the opportunity: a different starting electronic structure produces models with new symmetries and new possibilities for simulating interacting electrons. The new catalog greatly expands the range of starting points for such discoveries.
“A small twist can change the balance between electrons’ motion and their interactions. Different materials give us different ways to tune that balance and look for collective quantum behavior,” said coauthor Hanqi Pi, of the Donostia International Physics Center.
The researchers calculated selected twisted bilayers and found narrow bands in compounds including tin diselenide and hafnium disulfide. They also grew bulk crystals of these compounds, tin disulfide, gallium telluride and zirconium nitride chloride.
“We have already grown several of the promising materials. Connecting the catalog to crystal growth and exfoliation gives us a practical route from an electronic structure on a computer to a sample in the laboratory,” said coauthor Leslie M. Schoop, professor of chemistry and director of Princeton Center for Complex Materials at Princeton.
Initial sample preparation confirmed that the grown materials can be exfoliated—peeled down—to single layers.
“Some of these candidates are already crystals we can grow and peel down to a single layer. That gives experiments a concrete starting point for making new twisted structures and testing the physics predicted for them,” coauthor Kin Fai Mak of Cornell University noted.
The catalog identifies candidates by their electronic suitability for twisting; the next step is to assemble the layers into devices and test their collective behavior.
“Once we have the layers, we can work toward assembling devices and controlling their twist and electron density. Each new material gives us a different setting in which to look for collective states,” said coauthor Dmitri K. Efetov of Ludwig Maximilian University of Munich and the Munich Center for Quantum Science and Technology.
The shared database, built by Princeton physics researcher Nicolas Regnault, lets researchers compare the individual layers and select candidates for the physics they want to investigate.
“The value of a catalog is what people can do with it. Researchers can compare the electronic structures, select candidates for the physics they want to study, and bring their own questions to the search,” Regnault explained, who is also affiliated with the Flatiron Institute, the École normale supérieure in Paris and the French National Centre for Scientific Research.
The first catalog supplies the individual building blocks; the second helps researchers choose which ones to twist.
“We would like to take a problem about interacting electrons and ask which crystal, which layers and which twist will let us study it. The exciting part is that an experiment can also show us something we did not know to ask,” Bernevig concluded.
The two studies are the work of a joint theoretical and experimental team that spans more than a dozen institutions. At Princeton are: B. Andrei Bernevig (also DIPC and IKERBASQUE), Dumitru Călugăru (also the University of Oxford), Haoyu Hu (also the University of Science and Technology of China), Nicolas Regnault (also the Flatiron Institute and, in Paris, the École normale supérieure and the French National Centre for Scientific Research), Grigorii Skorupskii, Jiaze Xie and Leslie M. Schoop; at the Donostia International Physics: Center (DIPC), Yi Jiang, Hanqi Pi, Garen Avedissian, Yongsong Wang, Miguel M. Ugeda (also IKERBASQUE) and Maia G. Vergniory (also the Université de Sherbrooke); at the University of the Basque Country: Urko Petralanda and Luis Elcoro; at the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg: Angel Rubio (also the Flatiron Institute and the University of the Basque Country) and Lede Xian (also the Tsientang Institute for Advanced Study and the Songshan-Lake Materials Laboratory); at RWTH Aachen University: Dante M. Kennes (also the Max Planck Institute in Hamburg); at Sichuan Normal University: Qiaoling Xu (also the Tsientang Institute for Advanced Study); and at the University of Pennsylvania: Martin Claassen.
The experimental work involves Peter Höhn, Vicky Haase and Claudia Felser at the Max Planck Institute for Chemical Physics of Solids in Dresden; Rose Albu Mustaf and Emilia Morosan at Rice University; Jiacheng Zhu, Dongyang Yang, Zuhan Geng, Jie Shan and Kin Fai Mak at Cornell University, with Shan and Mak also at the Kavli Institute at Cornell for Nanoscale Science and Yang, Geng, Shan and Mak at the Max Planck Institute in Hamburg; and Abdelmajid Ouahchi, Soumyajit Samal and Dmitri K. Efetov at Ludwig Maximilian University of Munich, with Ouahchi also at the Technical University of Munich and Samal and Efetov at the Munich Center for Quantum Science and Technology.
The publicly available preprints are “Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials,” by Urko Petralanda, Yi Jiang, B. Andrei Bernevig, Nicolas Regnault and Luis Elcoro ( arXiv:2411.08950 ), and “2D Theoretically Twistable Material Database,” by Yi Jiang and colleagues ( arXiv:2411.09741 ).
Science
Computational simulation/modeling
Not applicable
2D Theoretically Twistable Material Database
24-Sep-2026
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