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Mathematical model sheds light on how exercise suppresses tumour growth

Physical exercise plays an important role in controlling disease, including cancer, due to its effect on the human body’s immune system. A research team from the USA and India has now developed a mathematical model to quantitatively investigate the complex relationship between exercise, immune function and cancer.

Exercise is thought to supress tumour growth by activating the body’s natural killer (NK) cells. In particular, skeletal muscle contractions drive the release of interleukin-6 (IL-6), which causes NK cells to shift from an inactive to an active state. The activated NK cells can then infiltrate and kill tumour cells. To investigate this process in more depth, the team developed a mathematical model describing the transition of a NK cell from its inactive to active state, at a rate driven by exercise-induced IL-6 levels.

“We developed this model to study how the interplay of exercise intensity and exercise duration can lead to tumour suppression and how the parameters associated with these exercise features can be tuned to get optimal suppression,” explains senior author Niraj Kumar from the University of Massachusetts Boston.

Impact of exercise intensity and duration

The model, reported in Physical Biology, is constructed from three ordinary differential equations that describe the temporal evolution of the number of inactive NK cells, active NK cells and tumour cells, as functions of the growth rates, death rates, switching rates (for NK cells) and the rate of tumour cell kill by activated NK cells.

Kumar and collaborators – Jay Taylor at Northeastern University and T Bagarti at Tata Steel’s Graphene Center – first investigated how exercise intensity impacts tumour suppression. They used their model to determine the evolution over time of tumour cells for different values of α0 – a parameter that correlates with the maximum level of IL-6 and increases with increased exercise intensity.

Temporal evolution of tumour cells
Modelling suppression Temporal evolution of tumour cells for different values of α0 (left) and exercise time scale τ (right). (Courtesy: J Taylor et al Phys. Biol. 10.1088/1478-3975/ad899d)

Simulating tumour growth over 20 days showed that the tumour population increased non-monotonically, exhibiting a minimum population (maximum tumour suppression) at a certain critical time before increasing and then reaching a steady-state value in the long term. At all time points, the largest tumour population was seen for the no-exercise case, confirming the premise that exercise helps suppress tumour growth.

The model revealed that as the intensity of the exercise increased, the level of tumour suppression increased alongside, due to the larger number of active NK cells. In addition, greater exercise intensity sustained tumour suppression for a longer time. The researchers also observed that if the initial tumour population was closer to the steady state, the effect of exercise on tumour suppression was reduced.

Next, the team examined the effect of exercise duration, by calculating tumour evolution over time for varying exercise time scales. Again, the tumour population showed non-monotonic growth with a minimum population at a certain critical time and a maximum population in the no-exercise case.  The maximum level of tumour suppression increased with increasing exercise duration.

Finally, the researchers analysed how multiple bouts of exercise impact tumour suppression, modelling a series of alternating exercise and rest periods. The model revealed that the effect of exercise on maximum tumour suppression exhibits a threshold response with exercise frequency. Up to a critical frequency, which varies with exercise intensity, the maximum tumour suppression doesn’t change. However, if the exercise frequency exceeds the critical frequency, it leads to a corresponding increase in maximum tumour suppression.

Clinical potential

Overall, the model demonstrated that increasing the intensity or duration of exercise leads to greater and sustained tumour suppression. It also showed that manipulating exercise frequency and intensity within multiple exercise bouts had a pronounced effect on tumour evolution.

These results highlight the model’s potential to guide the integration of exercise into a patient’s cancer treatment programme. While still at the early development stage, the model offers valuable insight into how exercise can influence immune responses. And as Taylor points out, as more experimental data become available, the model has potential for further extension.

“In the future, the model could be adapted for clinical use by testing its predictions in human trials,” he explains. “For now, it provides a foundation for designing exercise regimens that could optimize immune function and tumour suppression in cancer patients, based on the exercise intensity and duration.”

Next, the researchers plan to extend the model to incorporate both exercise and chemotherapy dosing. They will also explore how heterogeneity in the tumour population can influence tumour suppression.

The post Mathematical model sheds light on how exercise suppresses tumour growth appeared first on Physics World.

US ploughs $50m into sodium-ion battery development

The US Department of Energy (DOE) has awarded $50m to a consortium of national laboratories and universities to develop sodium-ion batteries as a sustainable, low-cost alternative to lithium-ion technology.

Lithium-ion batteries currently dominate the electric-vehicle market and they are also used in smartphones and to store energy from renewable source such as wind and solar. Yet relying on a single battery technology such as lithium-ion creates dependencies on critical elements such as lithium, cobalt and nickel.

Sodium, however, is an abundant, inexpensive element and offers a promising way to diversify battery materials. The downside is that sodium-ion batteries currently store less energy per unit weight and volume than lithium-ion batteries.

The money from the DOE over the next five years will be used to create the Low-cost Earth-abundant Na-ion Storage (LENS) consortium. LENS will be led by Argonne National Laboratory and includes five other DOE national laboratories such as Brookhaven, Lawrence Berkely and Sandia as well eight US universities.

By leading the LENS consortium, Argonne will push sodium-ion battery technology forward and contribute to a secure energy future for everyone,” notes Argonne director Paul Kearns. ​Our scientific expertise and dynamic collaborations in this important field will strengthen US competitiveness.”

The LENS consortium will now develop high-energy electrode materials and electrolytes for sodium-ion batteries as well as design, integrate and benchmark battery cells with the aim of creating high-energy, long-lasting batteries.

“The challenge ahead is improving sodium-ion energy density so that it first matches and then exceeds that of phosphate-based lithium-ion batteries while minimizing and eliminating the use of all critical elements,” says LENS consortium director Venkat Srinivasan.

  • Venkat Srinivasan, William Mustain and Martin Freer appeared on a Physics World Live panel discussion about battery technology held on 21 November 2024, which you can watch online now

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A ‘quantum rose’ for the 21st century: Oksana Kondratyeva on her stained-glass art inspired by a quantum computer

Stained glass is the most “physical” of all art forms. If you’ve ever been inside Chartres Cathedral in France or York Minster in the UK, you’ll know how such glass can transform a building by turning sunlight into gloriously captivating multicoloured patterns. What you might not realize, however, is that centuries of scientific innovation have forged this form of art.

Byzantine glaziers started making leaded glass windows back in the 6th century CE before the technique spread widely across Europe. But our ability to stain glass only emerged in the 14th century when medieval alchemists found that coating glass with silver nitrate and firing it in a kiln gave the material a range of orange and yellow hues.

Later, a range of other techniques were developed to produce various decorative effects, with stained glass becoming both an art and a craft. Particularly important has been the use of hydrofluoric acid – a poisonous and highly corrosive liquid – to strip off the surface of glass, layer by layer, to alter its colour and thickness.

Known as hydrofluoric acid etching, the technique is widely used by modern architectural glass artists. Beautiful patterns can be created by altering the strength and temperature of the acid and varying the time for which the glass is exposed to it. Materials like wax, bitumen and lead foil can also be used as resists to leave parts of the glass untouched.

Like other “glass artists”, I am an experimentalist of sorts. We use an empirical knowledge of glass to make beautiful objects – and sometimes even make new discoveries

Like other “glass artists”, I am an experimentalist of sorts. We use an empirical knowledge of glass to make beautiful objects – and sometimes even make new discoveries. In fact, some historians say that hydrofluoric acid was first created in 1670 by a German glassworker named Heinrich Schwanhardt.

While treating a mineral called fluorspar with acid, he saw that the lenses in his spectacles went cloudy – prompting him to start using the same reaction to etch glass. Only much later – in the late 18th century – did chemists carry out “proper” lab experiments to show that flourspar (calcium fluoride) reacts with the acid to create what we now call hydrofluoric acid.

From the 19th century onwards, acid-etching techniques started to be used by numerous stained-glass artists and studios throughout Britain and Ireland. Dublin-born Harry Clarke (1889–1931) was the leading proponent of the hydrofluoric acid-etching technique, which he mastered in an exceptionally personal and imaginative manner.

Art of glass

I first came across acid etching in 2010 while studying glass and architecture at Central Saint Martins, which is part of the University of the Arts London. The technique intrigued me and I started wondering about its origins and how it works, from a scientific point of view. What chemical processes are involved? What happens if you vary how the acid is applied? And how can that create new decorative effects?

A glass artwork in a large gallery space with light shining through and reflecting colours on the floor
Meet the art Per scientiam ad astra by Oksana Kondratyeva on display at the Ruskin Glass Centre in the UK, home to the 2024 British Glass Biennale in Stourbridge, near Birmingham, UK. (Courtesy: Oksana Kondratyeva)

Unable to find full answers to my questions, I started carrying out my own experiments and investigations. I wanted to understand how fluorspar – which can be colourless, deep green or even purple – can be turned into hydrofluoric acid and what goes on at a chemical level when it etches glass.

During my investigations, which I published in 2014 in The Journal of Stained Glass (38 146), I was astonished to find references to glass in the famous lectures given by Richard Feynman about quantum electrodynamics. Published in book form as QED: the Strange Theory of Light and Matter, Feynman explained the partial reflection of light by experimenting with blocks of glass.

He showed that the amount of light reflected increases with the thickness of the glass, pointing out that photons interact with electrons throughout the material, not just on the surface. “A piece of glass,” Feynman wrote, “is a terrible monster of complexity – huge numbers of electrons are jiggling about.”

In my own work, I’ve recently been experimenting with glass of different thickness to make a piece of art inspired by the packaging for a quantum chip made by Rigetti Computing. Entitled Per scientiam ad astra (through science to the stars), the artwork was displayed at the 2024 British Glass Biennale at the Ruskin Glass Centre in Stourbridge, UK – a historically significant area for glass-making that pioneered the creation of etched glass in the 19th century.

Rigetti Computing’s quantum chip

A quantum computer and a macro shot of the container for the microchip
Art from science (left) The packaging for Rigetti Computing’s quantum chip that inspired the stained-glass artwork made by Oksana Kondratyeva. (right) The Rigetti quantum computer, with packaging visible at the bottom attached to the input/output plate. (Courtesy: Rigetti Computing)

The quantum computers developed by US firm Rigetti Computing are based on superconducting qubits made from materials such as aluminium, indium and niobium. The qubits are manufactured using a mix of novel fabrication methods and well-established semiconductor and micro-electromechanical systems (MEMS) processing techniques. The quantum chip – containing the qubits and other components such as readout resonators – are carefully assembled inside a gold-plated copper packaging that connects it to a printed circuit board (PCB).

The PCB in turn routes the signals to microwave connectors, with the whole system cooled to below 10 millikelvin using dilution refrigeration. The environment in which the quantum bits operate is carefully engineered so that they don’t lose their coherence. Rigetti’s design could, in principle, be scaled up to create much larger and more reliable quantum processors with many more qubits.

The packaging for the quantum chip, on which Oksana Kondratyeva’s artwork is based, is a disc 81.5 mm in diameter and 12 mm deep (see image). With the chip at its centre, the packaging is mounted at the bottom of a tower-like structure that, along with the rest of the fridge and wiring, forms the fully assembled quantum computer. Signals are delivered to and from the chip to drive qubit operations and return measured results.

A quantum rose

Creating an artwork based on quantum technology might be an unusual thing to do, but when I saw a photo of the packaging for a quantum chip back in 2020, I was astounded by the elegant geometry of this enigmatic object, which holds the “brain” of the company’s quantum computer (see box above). Reminding me of the beautiful circular rose windows of medieval cathedrals, I wanted to use glass to create a “quantum rose” for the 21st century. Later, Rigetti got in touch with me after my plans were reported on in Physics World in June 2022.

Two photos: small detail of blue stained glass; full glass artwork covered with lines and arrows drawn in pen
A closer look (left) Per scientiam ad astra was created by Oksana Kondratyeva etching mouth-blown glass with hydrofluoric acid. Each fragment of the artwork was individually acid-etched and leaded. (right) The arrows are “vectors of light” that were temporarily marked by Kondratyeva onto the glass as a guide for the layered acid-etching, reflecting her artistic thought. (Courtesy: Oksana Kondratyeva)

As you can imagine, hydrofluoric acid etching is an extremely dangerous technique, given how corrosive the liquid is. I acid-etch glass from the German company LambertsGlas in a specially equipped studio with a ventilation cabinet to extract fumes and I wear a protective suit with a respiratory mask. As you can see from the video below, I look more like an astronaut than an artist.

Acid etching can be done in lots of different ways (see Materials Today Proceedings 55 56) – but I prefer to apply the acid freely with a cotton or plastic brush, coining my technique “acid painting”. The resulting artwork, which took me several months to make, is just over a metre in diameter.

  • This video has no voice over.     (Video courtesy: Space Production)

Mostly blue with a red focal point, the artwork constantly changes as you move around it. Visitors to the British Glass Biennale seemed to be attracted to it, with comments such as “empowering” and “ethereal”. Per scientiam ad astra will now move to a private residence that just happens to be not far from the UK’s National Quantum Computing Centre in Oxfordshire, where one of Rigetti’s quantum computers is housed.

Art–science crossover

Stained-glass windows were once “illuminated books” for people who could not read – mysterious transmitters of knowledge that told stories about human life. The same, in a way, is true of quantum computers, which are broadening our understanding of reality. And just as mathematical equations can have an inner beauty, so too do quantum computers through the myriad technological innovations that underpin them.

With 2025 being the International Year of Quantum Science and Technology, I hope my artwork raises interesting questions at the intersection between art and science, continuing the “two-cultures” dialogue introduced by C P Snow in 1959. Is it a metaphorical window into the secret architecture of the universe? Or is it a visualization of our reality, where Newtonian and quantum-mechanical worlds merge?

Working with stained glass requires an understanding of how materials behave but that knowledge will only get you so far. To reveal new regions of reality and its beauty, unexpectedness plays a role too. Stained-glass art is the convergence of certainty and uncertainty, where science and art come together. Art can unite people; and through the beauty in art, we can create a better reality.

This article forms part of Physics World‘s contribution to the 2025 International Year of Quantum Science and Technology (IYQ), which aims to raise global awareness of quantum physics and its applications.

Stayed tuned to Physics World and our international partners throughout the next 12 months for more coverage of the IYQ.

The post A ‘quantum rose’ for the 21st century: Oksana Kondratyeva on her stained-glass art inspired by a quantum computer appeared first on Physics World.

Nuclear shape transitions visualized for the first time

Diagram showing a xenon atom changing shape from spherical to prolate to triaxial to oblate during a collision at the LHC
Shape shifter: The nucleus of the xenon atom can assume different shapes depending on the balance of internal forces at play. When two xenon atoms collide at the LHC, simulations indicate that the extremely hot conditions will trigger changes in these shapes. (Courtesy: You Zhou, NBI)

Xenon nuclei change shape as they collide, transforming from soft, oval-shaped particles to rigid, spherical ones. This finding, which is based on simulations of experiments at CERN’s Large Hadron Collider (LHC), provides a first look at how the shapes of atomic nuclei respond to extreme conditions. While the technique is still at the theoretical stage, physicists at the Niels Bohr Institute (NBI) in Denmark and Peking University in China say that ultra-relativistic nuclear collisions at the LHC could allow for the first experimental observations of these so-called nuclear shape phase transitions.

The nucleus of an atom is made up of protons and neutrons, which are collectively known as nucleons. Like electrons, nucleons exist in different energy levels, or shells. To minimize the energy of the system, these shells take different shapes, with possibilities including pear, spherical, oval or peanut-shell-like formations. These shapes affect many properties of the atomic nucleus as well as nuclear processes such as the strong interactions between protons and neutrons. Being able to identify them is thus very useful for predicting how nuclei will behave.

Colliding pairs of 129Xe atoms at the LHC

In the new work, a team led by You Zhou at the NBI and Huichao Song at Peking University studied xenon-129 (129Xe). This isotope has 54 protons and 75 neutrons and is considered a relatively large atom, making its nuclear shape easier, in principle, to study than that of smaller atoms.

Usually, the nucleus of xenon-129 is oval-shaped (technically, it is a 𝛾-soft rotor). However, low-energy nuclear theory predicts that it can transition to a spherical, prolate or oblate shape under certain conditions. “We propose that to probe this change (called a shape phase transition), we could collide pairs of 129Xe atoms at the LHC and use the information we obtain to extract the geometry and shape of the initial colliding nuclei,” Zhou explains. “Probing these initial conditions would then reveal the shape of the 129Xe atoms after they had collided.”

A quark-gluon plasma

To test the viability of such experiments, the researchers simulated accelerating atoms to near relativistic speeds, equivalent to the energies involved in a typical particle-physics experiment at the LHC. At these energies, when nuclei collide with each other, their constituent protons and neutrons break down into smaller particles. These smaller particles are mainly quarks and gluons, and together they form a quark-gluon plasma, which is a liquid with virtually no viscosity.

Zhou, Song and colleagues modelled the properties of this “almost perfect” liquid using an advanced hydrodynamic model they developed called IBBE-VISHNU. According to these analyses, the Xe nuclei go from being soft and oval-shaped to rigid and spherical as they collide.

Studying shape transitions was not initially part of the researchers’ plan. The original aim of their work was to study conditions that prevailed in the first 10-6 seconds after the Big Bang, when the very early universe is thought to have been filled with a quark-gluon plasma of the type produced at the LHC. But after they realized that their simulations could shed light on a different topic, they shifted course.

“Our new study was initiated to address the open question of how nuclear shape transitions manifest in high-energy collisions,” Zhou explains, “and we also wanted to provide experimental insights into existing theoretical nuclear structure predictions.”

One of the team’s greatest difficulties lay in developing the complex models required to account for nuclear deformation and probe the structure of xenon and its fluctuations, Zhou tells Physics World. “There was also a need for compelling new observables that allow for a direct probe of the shape of the colliding nuclei,” he says.

Applications in both high- and low-energy nuclear and structure physics

The work could advance our understanding of fundamental nuclear properties and the operation of the theory of quantum chromodynamics (QCD) under extreme conditions, Zhou adds. “The insights gleaned from this work could guide future nuclear collision experiments and influence our understanding of nuclear phase transitions, with applications extending to both high-energy nuclear physics and low-energy nuclear structure physics,” he says.

The NBI/Peking University researchers say that future experiments could validate the nuclear shape phase transitions they observed in their simulations. Expanding the study to other nuclei that could be collided at the LHC is also on the cards, says Zhou. “This could deepen our understanding of nuclear structure at ultra-short timescales of 10-24 seconds.”

The research is published in Physical Review Letters.

The post Nuclear shape transitions visualized for the first time appeared first on Physics World.

From qubits to metamaterials: tech that led to Institute of Physics business awards 2024

I have mentioned many times in this column the value of the business awards given by the Institute of Physics (IOP), which can be a real “stamp of approval” for firms developing new technology. Having helped to select the 2024 winners, it was great to see eight companies winning a main IOP Business Innovation Award this time round, bringing the total number of firms honoured over the last 13 years to 86. Some have won awards on more than one occasion, with Fetu being one of the latest to join this elite group.

Set up by Jonathan Fenton in 2016, FeTu originally won an IOP Business Start-up Award in 2020 for its innovative Fenton Turbine. According to Fenton, who is chief executive, it is the closest we have ever got to the ideal, closed-cycle reversible heat engine first imagined by thermodynamics pioneer Nicolas Carnot in 1824. The turbine, the firm claims, could replace compressors, air conditioners, fridges, vacuum pumps and heat pumps with efficiency savings across the board.

Back in 2020, it might have sounded like a “too-good-to-be-true” technology, but Fenton has sensibly set out to prove that’s not the case, with some remarkable results. The turbine is complex to describe but the first version promised to cut the energy cost of compressing gases like air by 25%. They claim has already been proven in independent tests carried out by researchers at the University of Bath.

One challenge of any technology with many different applications is picking which to focus on first.

One challenge of any technology with many different applications is picking which to focus on first. Having decided to focus on a couple of unique selling factors in large markets, FeTu has now won a 2024 Business Innovation Award for developing a revolutionary heat engine that can generate electrical power from waste heat and geothermal sources as low as 40 °C. It has a huge market potential as it is currently not possible to do this economically.

Innovative ideas

Another winner of an IOP Business Innovation Award is Oxford Ionics,  a quantum-computing firm set up in 2019 by Chris Balance and Tom Harty after doing PhDs at the University of Oxford. Their firm’s qubits are based on trapped ions, which traditionally have been controlled with lasers. It’s an approach that works well for small processors, but becomes untenable and error-prone as the size of the processor scales, and the number of qubits increases.

Instead of lasers, Oxford Ionics’ trapped-ion processors use a proprietary, patented electronic system to control the qubits. It was for this system that the company was recognized by the IOP, along with its ability to scale the architecture so that the chips can be made in large quantities on standard semiconductor production lines. That’s essential if we are to build practical quantum computers.

Whilst it’s still early days in the commercialisation of quantum computing, Oxford Ionics is an exciting company to watch. It has already won contracts to supply the UK’s National Quantum Computing Centre at Harwell and has bagged a large contract with its partner Infineon Technologies AG in Munich to build a state-of-the-art portable quantum computer for Germany’s cybersecurity innovation agency. The two firms are one of three independent contractors selected by the agency, which is investing a total of €35m in the project.

I should also mention Dublin-based Equal1, which won the IOP’s £10,000 quantum Business Innovation and Growth (qBIG) Prize in 2024. Equal1 is developing rack-mountable quantum computers powered by a system that integrates quantum and classical components onto a single silicon chip using commercial fabrication processes. The company, which aims to develop compact quantum computers, also won 10 months of mentoring from the award’s sponsors Quantum Exponential.

Meanwhile, Covesion – a photonics and quantum components supplier founded in 2009 – has won an IOP Business Innovation Award for its magnesium-doped, periodically poled, lithium niobate (MgO:PPLN) crystals and waveguides. They allow light to be easily converted from one frequency to another, providing access to wavelengths that are not available from commercial laser sources.

With a manufacturing base in Southampton, Covesion works with customers and industry partners to help them design and make high quality MgO:PPLN products used in a wide range of applications. They include quantum computing, communication, sensing and timing; frequency doubling of femtosecond lasers; mid-infrared generation; atom cooling; terahertz generation and biomedical imaging. The shear breadth and global nature of the customer base is impressive.

Sounds promising

Among the companies to win an IOP Business Start-up Award is Metasonixx, based in Brighton. Spun off from the universities of Bristol and Sussex in 2019, the firm makes mass-produced acoustic metamaterial panels, which can dramatically attenuate sound (10 dB in its Sonoblind) and yet still allow air to flow freely (3 dB or 50% attenuation). That might seem counter-intuitive, but that’s where the innovation comes in and the panels can help with noise management and ventilation, allowing industrial ventilators and heat pumps to be more widely used.

Metasonixx Sonoblind Air
Sounds good Metasonixx is turning metamaterials into commercial reality as noise-abatement products. (Courtesy: Metasonixx Sonoblind Air)

The company really got going in 2020, when it got a grant from UK Research and Innovation to see if its metamaterials could cut noise in hospitals to help patients recovering from COVID-19 and improve the well-being of staff. After Metatronixx won the Armourers and Brasiers Venture Prize in 2021 for their successes on COVID wards, the firm decided to mass-produce panels that could perform as well as traditional noise-reduction solutions but are modular and greener, with one-third of the mass and occupying one-twelfth of the space.

From a physics point of view, panels that can let air and light through in this way are interferential filters, but working over four doublings of frequency (or octaves). With manufacturing and first sales in 2023, their desk separators are now being tested in noisy offices worldwide. Metatronixx believes its products, which allow air to flow through them, could help to boost the use of industrial ventilators and heat pumps, thereby helping in the quest to meet net-zero targets.

Winning awards for Metasonixx is not a new experience, having also picked up a “Seal of Exellence Award” from the European Commission in 2023 and honoured at Bristol’s Tech-Xpo in 2024. Its new IOP award will sit very nicely in this innovative company’s trophy cabinet.

  • In his next article, James McKenzie will look at the rest of the 2024 IOP Business Award winners in imaging and medical technology.

The post From qubits to metamaterials: tech that led to Institute of Physics business awards 2024 appeared first on Physics World.

Physicists close in on fractionally-charged electron mystery in graphene

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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