Twisting 2D nanomaterials unlocks exotic quantum phases of matter

From superconductivity to fractional charge, strange and exotic states emerge when 2D nanomaterial bilayers are twisted into moiré superlattice structures. Chemists are joining force with physicists to explore a strange twisted world

Article summary

Twistronics studies what happens when two atomically thin materials, especially graphene, are stacked and rotated slightly, creating moiré superlattices that can dramatically alter electronic properties. A small twist can transform materials into magnets, insulators, conductors or even superconductors.

The field gained major attention after the discovery that bilayer graphene twisted to the “magic angle” of 1.1° develops flat electronic bands and becomes superconducting at very low temperatures. These strongly correlated electronic states continue to challenge existing theories and have revealed a range of unexpected quantum phenomena.

Researchers are now extending twistronics beyond graphene to materials such as halide perovskites, transition metal dichalcogenides and MXenes. These systems are exhibiting unusual behaviours, including altered exciton transport, exotic superconductivity and other novel electronic effects that could not be achieved in conventional crystals.

New experimental tools, including quantum twisting microscopes that can vary twist angles in situ, are helping scientists explore previously inaccessible quantum states, such as fractional quantum Hall-like phases without strong magnetic fields. While practical applications remain distant, the research could ultimately aid the development of topological quantum computing and potentially guide the design of room-temperature superconductors. This summary was generated by AI and checked by a human editor

Few chemical structures are as instantly recognisable as graphene. The orderly honeycomb construction of this two-dimensional carbon nanosheet has become very familiar to physicists and chemists alike.

Yet two decades after its discovery, graphene continues to surprise. When two sheets of graphene are layered together, then twisted out of atomic alignment with the other, the familiar honeycomb appearance dissolves.

As the twist angle changes, the complex patterns the two offset sheets create move from intricate mosaic-like arrangements to arrays of giant hexagons. In each case, the repeating nature of each sheet of graphene’s structure remains, but translated into periodic pattern of far grander scale.

The visual effect of this twist, known as a moiré pattern, is not unique to two-dimensional nanomaterials. ‘Moiré patterns also appear at macroscale,’ says materials chemist Yury Gogotsi from Drexel University in Philadelphia, US. When 2D nanomaterials are twisted into a moiré superlattice structure, however, their properties also change, sometimes inverting completely.

A tiny twist can turn a non-magnet into a magnet, or an insulator into a conductor. In the case of graphene, it can turn a conductor into a superconductor. ‘When people discovered that you could take two layers of non-superconducting material, twist it by roughly one degree and it becomes superconductor, that captured the imagination,’ says Gogotsi.

In 2026, condensed matter physicists Eva Andrei, Pablo Jarillo-Herrero and Allan MacDonald were awarded the Kavli prize in nanoscience for the work that led to the 2018 discovery of superconductivity in magic angle moiré superlattice graphene. The scene has only got wilder since, says Dahlia Klein from the University of Chicago, US, who was a PhD student in Jarillo-Herrero’s MIT lab at the time of the 2018 discovery.

As more 2D nanomaterials have been combined and twisted, exotic new quantum phases of matter have emerged – some long hypothesised by theory, others never predicted and currently confounding explanation. ‘With some of these phases, there is no existing framework to even describe it,’ Klein says.

Chemists are increasingly joining the fun, twisting more complex 2D nanomaterials from covalent organic frameworks (COFs) to MXenes and measuring the effects. ‘If you can exfoliate it, it is being twisted somewhere in the world right now,’ says Klein.

Magic-angle graphene and flat bands

When Klein joined Jarillo-Herrero’s lab as a graduate student in 2015 after completing her master’s in chemistry, her focus was on growing 2D materials with novel properties. ‘That work ended up with us being part of the team that discovered the first 2D magnets,’ Klein says. ‘Now, of course, people are twisting 2D magnets and having their own fun, seeing if we can get magnetic textures that wouldn’t exist on their own in a crystal.’

Klein joined the magic angle graphene project toward the end of her PhD. The first hints that twisted graphene bilayers gained unusual electronic properties had come almost a decade earlier. Studying graphene using scanning tunnelling microscopy (STM), Andrei and her team at Rutgers University were the first to look not only at the moiré structures in twisted graphene bilayers, but at how the twist affects the material’s properties.

As the atoms in the two graphene layers are twisted out of alignment, the material’s electronic structure changes alongside the moiré pattern, the team discovered. Most remarkably, at the magic twist angle of 1.1°, bilayer graphene entered the rare, fabled ‘flat band’ electronic state.

Whereas chemists generally think of electronic structure in terms of energy levels, condensed matter physicists think in electronic bands. Plotted as a graph with energy on the y-axis and momentum on the x, electronic bands are typically wavy, reflecting the dispersion in velocity of electrons moving through a crystal.

Graphene only has a flat band at 1.1°, and that’s where all the magic happens

A flat electronic band denotes the strange scenario that the electrons’ velocity has slowed almost to nothing. ‘The electrons are not zipping around the material like in a normal metal,’ Klein says. ‘Their kinetic energy is quenched, close to zero.’ In this state, the electron–electron Coulomb interactions dominate. And that’s when the fun begins, she says.

‘In condensed matter, the smoking gun for interesting phases is a flat band,’ says Klein. ‘And the thing is, graphene doesn’t have a flat band – it is only at this specific angle of 1.1° that the top and bottom graphene layers hybridise to form this flat band, and that’s where all the magic happens.’

The form that magic takes is often a surprise. ‘Theory has been very good at predicting where there will be flat bands, but poor at describing which of the many competing phases will win in these “strongly correlated” regimes,’ Klein says. When the Jarillo–Herrero group succeeded in making bilayer graphene at the magic 1.1° angle, they didn’t know what properties might materialise.

‘The discovery of superconductivity was a true surprise – and there’s still no consensus on the mechanism,’ Klein says. Magic angle bilayer graphene’s superconductivity, which arises below 1.7K, relates to the way electrons in the flat band form tightly bonded pairs, but the mechanism behind this pairing remains unclear.

Even above the superconductivity critical temperature, magic angle bilayer graphene’s properties puzzle. Its electrical resistance increases linearly with temperature over a much wider range than is observed in conventional metals. ‘The same fingerprint appears in high-temperature superconducting cuprates, where it has resisted explanation for 40 years,’ Klein says. ‘Nobody predicted it here, and its origin is still debated.’

Difficult to explain superconducting behaviour has also emerged in other ‘twistronic’ moiré system 2D nanomaterial bilayers, including tungsten diselenide. Superconductivity signatures observed in twisted molybdenum ditelluride ‘may point to a genuinely exotic pairing mechanism’, Klein says.

Twisted perovskite bilayers

Twistronics was initially the preserve of condensed matter physics, but chemists have been paying attention. ‘We noticed that most of the work on twisted 2D materials was done on very simple materials – graphene, and transition metal dichalcogenides such as molybdenum or tungsten diselenide – which are all based on the same type of hexagonal crystal lattice with six-fold symmetry,’ says Letian Dou, a materials chemist at Emory University in Georgia, US. ‘As chemists, we wondered, could other materials also give interesting properties?’

Dou synthesises and studies the structure–property relationships of halide perovskites, materials that have been in the solar cell research spotlight due to their strong interactions with light. For Dou, twisted bilayer 2D perovskites was an obvious avenue for exploration.

Just making high-quality single crystal 2D perovskite sheets large enough to stack, twist and study, is a challenge. ‘Perovskite is intrinsically a 3D crystal, it’s very hard to only promote growth on the in-plane direction,’ says Dou. ‘So, we took another approach.’

The team developed an equilibrium-based process for exfoliating ultrathin sheets of methylammonium lead iodide perovskite from a crystalline precursor, triggered by adding a bulky organic surfactant. ‘Once we remove that surfactant, we can make perovskite sheets with a few nanometres thickness, and stack them to study the coupling,’ says Dou.

The team discovered unusual behaviours when probing the resultant moiré perovskites with lasers. Using pump–probe photoluminescence imaging, they generate excitons – excited-state electron–hole pairs – in the material and studied their diffusion. ‘Exciton mobility depended on the twist angle,’ Dou says. ‘Typically, excitons naturally diffuse – but in the 10° moiré material, they are frozen.’ Light emission from these stationary excitons was unusually strong.

The next step to exploring moiré perovskite properties is to make more robust variants that could withstand electrical contact, Dou says. ‘The first task is to make these materials more stable and more diverse,’ he says. Methylammonium lead iodide perovskite is very unstable when cut down to ultrathin slivers. ‘We are trying to make new structures that are intrinsically more stable,’ he says.

The quantum twisting microscope

Since joining the University of Chicago to start her independent research group in early 2026, Klein has been building a custom cryogenic scanning probe microscope called a quantum twisting microscope (QTM). The instrument, which builds on the moiré material microscopy techniques developed during her postdoc at the Weizmann Institute of Science in Rehovot, Isreal, will enable Klein and her team to twist 2D nanomaterial bilayers inside the microscope.

The technique exploits that relatively weak van der Waals interactions that stick graphene and related 2D nanomaterial bilayers together. Rather than place a pre-twisted bilayer moiré superlattice sample into the instrument, a single layer sample of 2D nanomaterial is added. The second layer of 2D nanomaterial is adhered to the microscope’s custom-made 3D-printed probe tip.

‘At the tip’s apex is a 2D contact area a few hundred nanometres in size,’ Klein says. Lowering the tip forms a localised bilayer where the apex meets the monolayer sample. Rotating the tip changes the angle between the two layers. ‘I like to think of it like a kaleidoscope,’ she says. ‘Rather than having to make a bunch of samples with different twist angles, now we can twist in situ and try to image what’s happening.’

Escaping some of the constraints of conventional materials synthesis and imaging is partly what makes moiré superlattice materials so compelling. Conventional materials have properties fixed by their constituent chemical bonds. ‘The landscape that electrons move through is defined by the potential set by the atoms in the crystal lattice,’ Klein says. ‘You’re stuck with that potential.’

The hybrid superlattice structures that emerge in moiré nanomaterials, however, offer a new way to play with electronic structure simply by adjusting the twist angle. ‘These larger superlattice potentials are renormalising the electronic landscape that the electrons sit in – and so it gives you this totally new tunability beyond changing chemical bonds.’

The much larger unit cell size of a moiré superlattice, compared to conventional crystal structure, also lets researchers play with the numbers of electrons populating that landscape. There’s no way you could add an extra electron per unit cell to a regular crystalline material where the unit cell might consist of just two atoms, Klein says. ‘You can’t add that much charge to a material, it wouldn’t hold it.’

But the superlattice structure of twisted moiré materials features much broader-scale periodicity, where a unit cell might contain 10,000 atoms. ‘It’s easy to add one electron per 10,000 atoms,’ Klein says. With a twist of the voltage knob on a scanning microscope, the full phase diagram of a moiré material can be mapped.

Fractional quantum anomalous Hall states

In topological moiré materials featuring flat bands, some of the strangest quantum phases behave as if they contain electrons that had been shattered into pieces and carry only a fraction of their usual single negative charge. Fractional variants of a phenomenon called the quantum Hall effect in moiré materials are the first time this behaviour has been seen outside of a strong magnetic field.

‘Fractional quantum anomalous Hall states [FQAH], with no magnet needed, were predicted for twisted molybdenum ditelluride and then measured experimentally in 2023,’ says Klein. Soon after, the related fractional quantum spin Hall (FQSH) phase was seen in the same material. ‘The FQSH effect was predicted some years back, but no one had predicted that this material would host it,’ Klein says. The finding, and the mechanism behind it, remains a topic of hot debate.

If we can understand these properties in a clean system, it could help us engineer an actual room temperature superconductor

This discovery of fractional materials that do not require a strong magnetic field potentially opens a pathway toward topological quantum computing. This mode of quantum computing has long been theorised, but until now there were no know materials that would permit the concept to be tried out.

Real world computers and devices remain a distant prospect. Moiré superlattice material assembly remains at the artisanal phase, involving pristine layers of material carefully peeled from high-quality single crystals. It’s a painstaking practice far removed from repeatable, scalable manufacture.

But today’s pristine, bespoke moiré systems offer a way to advance theory and understanding in related materials with real world promise – such as high temperature superconducting cuprates, which share many features with magic angle graphene. ‘If we can understand these properties in a clean system engineered through moiré heterostructures, it could help us engineer an actual room temperature superconductor using the design rules that we’re learning,’ Klein says.

Exploring chemical space to MXenes and COFs

Chemists are ideally positioned to develop methods that make moiré superlattice materials easier to make – both to accelerate their study in the short term, and perhaps usher them closer to real world applications in the long run.

One angle of research is to improve synthesis techniques for high-quality thin film material growth. The second is to continue exploring novel 2D moiré nanomaterials.

MXenes are some of the latest 2D nanomaterials to receive the twist treatment. These relatively complex materials consist of an early transition metal core, covered top and bottom with carbon or nitrogen and topped with surface-terminating functional groups such as halogens or hydroxyl groups.

This complexity lends MXenes some advantages over graphene, says Gogotsy, who co-led their discovery in 2011. ‘They are true metals, they are highly tuneable, there are almost infinite number of compositions, we can really control the surface chemistry,’ he says. But this complexity means large, high-quality MXene flakes are hard to make.

The first milestone in MXene moiré superlattice research was recently reached, when a team at Trinity College Dublin in Ireland used drop-casting to generate randomly overlapping single-layer MXene flakes. They scanned over the resulting samples with STM hunting for moiré patterns. It was a slow task, says Gogotsi, who collaborated on the project – but resulted in the discovery of three MXene moiré patterns. One exhibited hints of unusual electronic behaviour.

‘Can it lead to superconductivity? We don’t know yet,’ Gogotsi says. Conventional MXene synthesis generates materials with a disordered mixture of functional groups on its surface. The key to maximising electronic coupling between twisted MXene bilayers probably lies in controlling surface functionalisation, Gogotsi says – an area of strong recent progress in MXene research.

‘Nowadays we know how to make perfect MXene flakes with just single elements like chlorine or bromine on the surface,’ Gogotsi says. Theory predicts these materials should possess novel electronic properties, he says. ‘The challenge is to make those materials in sufficiently large flakes that one can twist them and do property measurements.’ More dedicated time at the MXene lab bench beckons.

‘When you go to terra incognita and discover something new, you never know how useful it’s going to be – but it’s always interesting,’ Gogotsi says. ‘And when chemists, physicists, materials scientists, electrical engineers all work together, there may be some exciting things coming out of all these activities.’

James Mitchell Crow is a science writer based in Melbourne, Australia