Physicists in the US have found an explanation for why electrons in a material called pentalayer moiré graphene carry fractional charges even in the absence of a magnetic field. This phenomenon is known as the fractional quantum anomalous Hall effect, and teams at the Massachusetts Institute of Technology (MIT), Johns Hopkins University and Harvard University/University of California, Berkeley have independently suggested that an interaction-induced topological “flat” band in the material’s electronic structure may be responsible.

Scientists already knew that electrons in graphene could, in effect, split into fractions of themselves in the presence of a very strong magnetic field. This is an example of the fractional quantum Hall effect, which occurs when a material’s Hall conductance is quantized at fractional multiples of e²/h.

In 2023, several teams of researchers introduced a new twist by observing this fractional quantization even without a magnetic field. The fractional quantum anomalous Hall effect, as it was dubbed, was initially observed in material called twisted molybdenum ditelluride (MoTe₂).

Then, in February this year, an MIT team led by physicist Long Ju spotted the same effect in pentalayer moiré graphene. This material consists of a layer of a two-dimensional hexagonal boron nitride (hBN) with five layers of graphene (carbon sheets just one atom thick) stacked on top of it. The graphene and hBN layers are twisted at a small angle with respect to each other, resulting in a moiré pattern that can induce conflicting properties such as superconductivity and insulating behaviour within the structure.

Answering questions

Although Ju and colleagues were the first to observe the fractional quantum anomalous Hall effect in graphene, their paper did not explain why it occurred. In the latest group of studies, other scientists have put forward a possible solution to the mystery.

According to MIT’s Senthil Todadri, the effect could stem from the fact that electrons in two-dimensional materials like graphene are confined in such small spaces that they start interacting strongly. This means that they can no longer be considered as independent charges that naturally repel each other. The Johns Hopkins team led by Ya-Hui Zhang and the Harvard/Berkeley team led by Ashvin Vishwanath and Daniel E Parker came to similar conclusions, and published their work in Physical Review Letters alongside that of the MIT team.

Crystal-like periodic patterns form an electronic “flat” band

Todadri and colleagues started their analyses with a reasonably realistic model of the pentalayer graphene. This model treats the inter-electron Coulomb repulsion in an approximate way, replacing the “push” of all the other electrons on any given electron with a single potential, Todadri explains. “Such a strategy is routinely employed in quantum mechanical calculations of, say, the structure of atoms, molecules or solids,” he notes.

The MIT physicists found that the moiré arrangement of pentalayer graphene induces a weak electron potential that forces electrons passing through it to arrange themselves in crystal-like periodic patterns that form a “flat” electronic band. This band is absent in calculations that do not account for electron–electron interactions, they say.

Such flat bands are especially interesting because electrons in them become “dispersionless” – that is, their kinetic energy is suppressed. As the electrons slow almost to a halt, their effective mass approaches infinity, leading to exotic topological phenomena as well as strongly correlated states of matter associated with high-temperature superconductivity and magnetism. Other quantum properties of solids such as fractional splitting of electrons can also occur.

“Mountain and valley” landscapes

So what causes the topological flat band in pentalayer graphene to form? The answer lies in the “mountain and valley” landscapes that naturally appear in the electronic crystal. Electrons in this material experience these landscapes as pseudo-magnetic fields, which affect their motion and, in effect, do away with the need to apply a real magnetic field to induce the fractional Hall quantization.

“This interaction-induced topological (‘valley-polarized Chern-1’) band is also predicted by our theory to occur in the four- and six-layer versions of multilayer graphene,” Todadri says. “These structures may then be expected to host phases where electron fractions appear.”

In this study, the MIT team presented only a crude treatment of the fractional states. Future work, Todadri says, may focus on understanding the precise role of the moiré potential produced by aligning the graphene with a substrate. One possibility, he suggests, is that it simply pins the topological electron crystal in place. However, it could also stabilize the crystal by tipping its energy to be lower than a competing liquid state. Another open question is whether these fractional electron phenomena at zero magnetic field require a periodic potential in the first place. “The important next question is to develop a better theoretical understanding of these states,” Todadri tells Physics World.

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A new type of composite material is 10 times more efficient at extracting gold from electronic waste than previous adsorbents. Developed by researchers in Singapore, the UK and China, the environmentally-friendly composite is made from graphene oxide and a natural biopolymer called chitosan, and it filters the gold without an external power source, making it an attractive alternative to older, more energy-intensive techniques.

Getting better at extracting gold from electronic waste, or e-waste, is desirable for two reasons. As well as reducing the volume of e-waste, it would lessen our reliance on mining and refining new gold, which involves environmentally hazardous materials such as activated carbon and cyanides. Electronic waste management is a relatively new field, however, and existing techniques like electrolysis are time-consuming and require a lot of energy.

A more efficient and suitable recovery process

Led by Kostya Novoselov and Daria Andreeva of the Institute for Functional Intelligent Materials at the National University of Singapore, the researchers chose graphene and chitosan because both have desirable characteristics for gold extraction. Graphene boasts a high surface area, making it ideal for adsorbing ions, they explain, while chitosan acts as a natural reducing agent, catalytically converting ionic gold into its solid metallic form.

While neither material is efficient enough to compete with conventional methods such as activated carbon on its own, Andreeva says they work well together. “By combining both of them, we enhance both the adsorption capacity of graphene and the catalytic reduction ability of chitosan,” she explains. “The result is a more efficient and suitable gold recovery process.”

High extraction efficiency

The researchers made the composite by getting one-dimensional chitosan macromolecules to self-assemble on two-dimensional flakes of graphene oxide. This assembly process triggers the formation of sites that bind gold ions. The enhanced extracting ability of the composite comes from the fact that the ion binding is cooperative, meaning that an ion binding at one site allows other ions to bind, too. The team had previously used similar methods in studies that focused on structures such as novel membranes with artificial ionic channels, anticorrosion coatings, sensors and actuators, switchable water valves and bioelectrochemical systems.

Once the gold ions are adsorbed onto the graphene surface, the chitosan catalyses the reduction of these ions, converting them from their ionic state into solid metallic gold, Andreeva explains. “This combined action of adsorption and reduction makes the process both highly efficient and environmentally friendly, as it avoids the use of harsh chemicals typically employed in gold recovery from electronic waste,” she says.

The researchers tested the material on a real waste mixture provided by SG Recycle Group SG3R, Pte, Ltd. Using this mixture, which contained gold in a residual concentration of just 3 ppm, they showed that the composite can extract nearly 17g/g of Au³⁺ ions and just over 6 g/g of Au⁺ from a solution – values that are 10 times larger than existing gold adsorbents. The material also has an extraction efficiency of above 99.5 percent by weight (wt%), breaking the current of limit of 75 wt%. To top it off, the ion extraction process is ultrafast, taking around just 10 minutes compared to days for other graphene-based adsorbents.

No applied voltage required

The researchers, who report their work in PNAS, say that the multidimensional architecture of the composite’s structure means that no applied voltage is required to adsorb and reduce gold ions. Instead, the technique relies solely on the chemisorption kinetics of gold ions on the heterogenous graphene oxide/chitosan nanoconfinement channels and the chemical reduction at multiple binding sites. The new process therefore offers a cleaner, more efficient and environmentally-friendly method for recovering gold from electronic waste, they add.

While the present work focused on gold, the team say the technique could be adapted to recover other valuable metals such as silver, platinum or palladium from electronic waste or even mining residues. And that is not all: as well as e-waste, the technology might be applied to a wider range of environmental cleaning efforts, such as filtering out heavy metals from polluted water sources or industrial effluents. “It thus provides a solution for reducing metal contamination in ecosystems,” Andreeva says.

Other possible applications areas, she adds, include sustainable decarbonization and hydrogen production, low-dimensional building blocks for embedding artificial neural networks in hardware for neuromorphic computing and biomedical applications.

The Singapore researchers are now studying how to regenerate and reuse the composite material itself, to further reduce waste and improve the process’s sustainability. “Our ongoing research is focusing on optimizing the material’s properties, bringing us closer to a scalable, eco-friendly solution for e-waste management and beyond,” Andreeva says.

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