In the 1980s, scientists measured quantized jumps in the energy of ions for the first time. In the 2000s, it was photons’ turn. Now, thanks to a tour de force of device engineering and nanofabrication, researchers at Stanford University in the US are reporting that phonons – mechanical vibrations like those that carry sound – also display this quantum behaviour.

“We could see it by eye [in the data], which was very satisfying,” team leader Amir Safavi-Naeini tells Physics World. “I’ve been fascinated with the interface between the quantum world and the classical world and trying to move that interface closer to daily experience…and now we have mechanical objects.”

Laying the groundwork

The Stanford team’s recipe for observing quantum jumps in phonons begins with thin films of lithium niobate (LiNbO₃). Although bulk samples of this material had been available since the 1950s, the commercialization of thin-film LiNbO₃ a decade ago was a game changer for Safavi-Naeini and his colleagues once they worked out how to process the material.

Because LiNbO₃ is piezoelectric, placing it under stress – from a vibration, say – produces a voltage. This voltage allows vibrational quanta to couple to superconducting qubits, after which the qubit states can be “read out” to determine whether a phonon was present or not.

The problem was that initially, the phonons had lifetimes of only 800 nanoseconds – well short of the millisecond the team needed to observe them falling from an excited state to the ground state. Extending these phonon coherence times “took a lot of work by a number of graduate students in my group,” Safavi-Naeini says.

After probing various sources of dissipation, including material properties that cause quantum excitations to lose coherence, the researchers realized that surface defects were key offenders. They therefore switched from polymer processing, which left a residue, to shadow masks that superimpose one chip over the other and evaporate metal through it. “There were probably three generations of students that worked on getting that four to five orders of magnitude increase in the performance of the devices,” Safavi-Naeini says.

Once they’d extended their phonon lifetimes, the researchers had to find a way of combining their “very clean, long-lived” mechanical and superconducting systems without destroying either. For this, Safavi-Naeini credits past and present students Takuma Makihara and Erik Szakiel, who spent most of their PhDs tackling issues with the mechanical oscillators before finding a way to couple them to the superconducting systems. “That was the last piece,” Safavi-Naeini recalls. “Once we had that, we could do these experiments.”

Spot the missing phonon

Because the superconducting qubits detect whether an even or odd number of phonons is present in the LiNbO₃ (which at very low energies amounts to determining whether a phonon is there at all), they are effectively performing a parity measurement. That could make the Stanford team’s system useful for quantum error correction, where the goal is to find out whether an error has crept in without actually measuring the quantum states, since doing so would destroy their useful quantum characteristics.

One of the most common sources of error in superconducting qubits is the loss of an excitation, such as when a phonon decays. However, if data is encoded into phonons in pairs and the system detects an odd number of them, this loss becomes apparent without measuring all the states. This so-called “binomial” code has already been implemented for microwave photons, and Safavi-Naeini explains that it works best for long-lived particles – a further benefit of the team’s long-lived phonons.

Protein and gravity measurements

The Stanford researchers are now collaborating with Michael Roukes and colleagues at the California Institute of Technology (Caltech) to explore possible applications in high-precision measurements of single protein masses. They are also interested in fundamental science questions such as whether it’s possible to generate entanglement between mechanical systems through gravitational fields.

However, Safavi-Naeini cautions that their phonon lifetimes would need to be much longer – a factor of 10 for error correction and mass spectrometry, and for gravity perhaps as much as six orders of magnitude, with further modifications to the experimental set-up also required – before they can achieve these goals. “The hope is that by figuring out the fundamental sources of loss in these materials we can build our way up to those experiments in the coming decade,” he says. “Every time you improve, you hit some new source of noise, you understand it, then you can deal with it, and then you go to the next one. It’s a fun physics problem.”

The research is published in Science.

The post Sound waves come in quantum jumps appeared first on Physics World.

In the mid-1970s a graduate student wrestling with a deceptively simple quantum problem uncovered one of the most haunting images in modern physics. The pattern seemed almost impossibly intricate: delicate wings assembled from infinitely nested bands and gaps, a self-similar pattern born from the motion of electrons in a crystal under a magnetic field. First published in 1976 (Phys. Rev. B 14 2239), it came to be known as Hofstadter’s butterfly, after its discoverer Douglas Hofstadter.

Half a century later, the butterfly has not faded into scientific nostalgia. If anything, it has become even more important – reappearing in new materials, new experiments and in places no-one imagined when it was first plotted. Recent research by Kazuki Ikeda from the University of Massachusetts and Yaron Oz at Stony Brook University suggests that related patterns may even surface in the physics of black holes (J. High Energy Phys. 2026 38).

Each new realization adds another chapter to a story that is not really about a single graph, or even a single discovery, but about the unity of patterns across the physical world. A structure first seen in a simple model has become a symbol of how richness can emerge from basic rules, how beauty can arise from constraint, and how the quantum world still harbours forms strange enough to surprise us.

How the butterfly got its wings

What makes Hofstadter’s butterfly so compelling is the remarkable story of its birth and, more importantly, how far it has travelled from its original birthplace. Like many scientific breakthroughs, its discovery was fairly obscure initially and owed a great deal to luck. In 1974 Hofstadter – son of the 1961 Nobel-prize-winning nuclear physicist Robert Hofstadter – had just dropped out of graduate school at Stanford University in the US and was “in despair” according to friend and physicist Francisco Claro.

Having just completed a PhD with the renowned solid-state physicist Gregory Wannier at the University of Oregon, Claro suggested that Hofstadter should approach Wannier as well. As it happened, Wannier had been struggling with a problem that had puzzled him for years: he could not obtain an analytical solution to Harper’s equation, which describes the motion of electrons on a 2D crystal lattice subjected to a perpendicular magnetic field.

Named after P G Harper, who was a graduate student of Rudolf Peierls at the University of Birmingham, UK, this classic “magnetic problem” displayed a mysterious sensitivity to whether the magnetic flux was a rational or irrational number. It was a feature that immediately captured Hofstadter’s imagination and, with the rational–irrational dichotomy echoing in his mind, Hofstadter began his PhD studies at Oregon by immersing himself in solving the problem.

But he soon found himself equally stuck. Frustrated by the analytical approaches often discussed at the time, he pursued a different path: numerical computation. Using a programmable Hewlett Packard desktop calculator that by today’s standards looks laughably primitive, he displayed the numerical solutions graphically as the energy of electrons versus magnetic flux Φ per unit cell of the lattice. At that moment, he became convinced that he had uncovered the true structure of the problem. “All at once my eyes were opened,” Hofstadter recalls.

What he found was a complex recursive shape (or fractal in today’s terminology) hidden within the energy spectrum of electrons in a magnetic field. Resembling a butterfly, Hofstadter brought his hand-plotted diagram, which he codenamed “Gplot”, to Wannier, who was not impressed. According to Hofstadter, Wannier dismissed the result as “numerology” and even threatened to withdraw the PhD student’s funding.

But after nearly a year, Wannier came to recognize the validity and significance of Hofstadter’s work, ultimately awarding Hofstadter his PhD and accepting the butterfly as a legitimate description of the energy spectrum of electrons moving on a 2D lattice in a magnetic field. Wannier even added to the butterfly’s story with a paper titled “A result not dependent on rationality for Bloch electrons in a magnetic field (Phys. Status Solidi b 88 757). This work, along with further studies with Claro, introduced a set of integers uniquely labelling every gap in the graph, providing a simplified description of the spectrum (Phys. Rev. B 19 6068).

Statements about states

Hofstadter’s butterfly is more than a beautiful graph. It is a map of what happens when quantum particles are caught between two competing kinds of order: the regular periodicity of a crystal lattice and the circular orbits of a magnetic field. When these two scales contend with one another, the energy spectrum does something extraordinary. Instead of varying smoothly, it fragments into a hierarchy of allowed and forbidden energies, referred to as bands and gaps, respectively.

Zoom in on one region and new structures emerge. Zoom in again and the pattern repeats, endlessly varied yet ruled by strict mathematical order. It is one of the rare instances in which fractal geometry appears not only in abstract mathematics or artistic imagination, but in the measurable behaviour of matter itself.

The deep connection between this theoretical pattern and real-world matter became clear through an exotic quantum phenomenon known as the integer quantum Hall effect. It was discovered experimentally by Klaus von Klitzing at the Max Planck Institute for Solid-State Physics in 1980 – a breakthrough that earned him the Nobel Prize in Physics five years later.

The classical Hall effect is what happens when a voltage is produced in a bulk conductor at right angles to an applied magnetic field. Similarly, the quantum Hall effect is the appearance of a voltage across opposite faces of a thin 2D semiconductor when a current is passed along the plane of the material and a magnetic field applied perpendicularly it. But there is one big difference in the quantum version.

If you slowly increase the power of the magnet, the transverse electrical conductance does not grow steadily. Instead, it jumps up sharply, with plateaus in between like steps on a staircase. In other words, it assumes quantized values given by integer multiples of the fundamental constant e²/h, where h is Planck’s constant and e is the charge on an electron.

In 1982 the British physicist David Thouless and his collaborators at the University of Washington, Seattle, made another remarkable discovery: the effect, they found, is topological. Topology is the study of the global properties of objects and topological invariants are those properties that do not change regardless of how much you try to deform a given object.

Thouless and colleagues found that the integers underlying the quantum Hall effect are topological invariants arising from the global topology of the electronic wave functions. This seminal work, which was published in 1982 (Phys. Rev. Lett. 49 405), significantly contributed to Thouless earning the 2016 Nobel Prize in Physics, which he shared with Duncan Haldane and Michael Kosterlitz for their work on “topological phase transitions and topological phases of matter”.

How all of this relates to Hofstadter’s butterfly is simple: the butterfly model describes all integer quantum Hall states, where the integers of Hall conductivity label the gaps in Hofstadter’s butterfly – the exact same integers that Wannier and Claro introduced in the butterfly spectrum (figure 1). In other words, the butterfly is not merely a chart of recursively split energy levels; it is also a coded map of topology in quantum matter under a magnetic field.

A pattern repeating across physics

That connection places it squarely within one of the central themes of modern condensed-matter physics, namely the realization that certain physical properties are protected not by local details, but by global features of the quantum state. But what is fascinating is that in the 50 years since Hofstadter’s butterfly was discovered, physicists have found that the same spectral architecture in it can also arise in a remarkable range of settings. It has appeared, for example, in other lattice geometries, in engineered semiconductor devices and in so-called moiré materials.

The butterfly’s migration into moiré systems has been especially fruitful. Such materials are created by stacking two atomically thin materials onto each other with a slight twist, creating a moiré pattern with different properties from the individual layers. Utilizing moiré materials, in research that began in 2013 led by Philip Kim of Columbia University (Nature 497 598) and continues apace with a team led by Ali Yazdani of Princeton University (Nature 639 60), the butterfly structure can now be tuned, probed and in some cases directly imaged on modern quantum platforms.

Over the last 50 years, the butterfly itself has also evolved into other forms. For instance, in some systems, the butterfly emerges without an external magnetic field. As a team of researchers led by Xu-Tao Wan from East China Normal University showed in 2025 (Phys. Rev. Lett. 136 033401), the fractal pattern can be controlled by twist angle – that is, by geometry alone.

Each time physicists add a new layer of realism – spin, interactions, periodic driving or lattice complexity – the butterfly adapts, and re-emerges in new forms, so long as it is not overwhelmed by strong interactions, disorder or thermal effects

In other realistic systems, electron spin – the particle’s intrinsic magnetic orientation, absent from the original simplified model – becomes an essential part of the physics. Even when a magnetic field splits the system into spin-up and spin-down states via Zeeman splitting, the butterfly spectrum survives. More striking still, the butterfly can emerge independently for each spin state, as Xiaomeng Liu and Zhida Liu of Cornell University discovered in 2025 (Nature Phys. 21 1873).

This persistence of the fractal structure, despite the added complexity introduced by spin, highlights the extraordinary robustness and universality of the underlying quantum phenomenon. More generally, what these new iterations of Hofstadter’s butterfly reveal is that what once looked like a specialized theoretical curiosity now seems more like a recurring motif in quantum matter.

Indeed, this is part of its enduring fascination: each time physicists add a new layer of realism – spin, interactions, periodic driving or lattice complexity – the butterfly adapts, and re-emerges in new forms, so long as it is not overwhelmed by strong interactions, disorder or thermal effects. This durability prompted a friend to once joke that whenever he undergoes an MRI scan, he cannot help wondering what kind of butterfly his body might be producing.

Beauty from simplicity

As my friend’s joke reveals, there is something unmistakably human about the butterfly’s appeal. Physicists are drawn to it not only for its usefulness, but for its beauty. It belongs to that rare class of scientific objects whose visual grace seems to gesture toward deeper truths. And yet its deepest charm may lie in the fact that its immense complexity grows from remarkable simplicity.

Beneath the intricate pattern are integers, recursion relations and number-theoretic structures that connect it to fairly simple geometric patterns, including the Farey tree, the tree of Pythagorean triplets and fractal packings such as the Apollonian gasket. In fact, this complicated quantum fractal admits a surprisingly simple geometric description: the butterfly landscape can be organized as a hierarchical lattice of trapezoids, bringing it into close parallel with geometric fractals such as the Sierpiński gasket (figure 2). It is extraordinary to think that this geometric harmony underlies such a complex and beautiful graph.

Fifty years on, Hofstadter’s butterfly remains exactly what great scientific ideas are supposed to be: elegant, prolific and unfinished. That interplay of beauty, mathematics and physical reality is what keeps the butterfly alive. Its evolution under interactions, spin effects and new forms of engineered geometry continues to reveal unexpected physics. And with each turn, the butterfly reminds us of something rare and precious in science: that the universe can hide immense complexity within simple forms, and that sometimes, if we are lucky, those forms are beautiful enough to be unforgettable.

The post Hofstadter’s butterfly turns 50: a fractal hiding in quantum matter appeared first on Physics World.

Multiferroics are materials that simultaneously exhibit two or more ferroic orders—stable arrangements of physical properties that can be switched using an external stimulus. These materials could be highly advantageous for the development of various technologies, including non-volatile, low-power memory devices, spintronic devices, miniaturized electronics, neuromorphic hardware, sensors and magnetoelectric devices.

When a material heats up, its electrical resistance often rises. The harder question is what, exactly, is getting in the way. The electrons carrying the current may be scattered by vibrations of the material's atomic lattice, known as phonons. They may also collide with one another. Frustratingly, a conventional temperature test warms the electrons and the lattice together, so the effects arrive tangled in the same resistance measurement.

When a material heats up, its electrical resistance often rises. The harder question is what, exactly, is getting in the way. The electrons carrying the current may be scattered by vibrations of the material's atomic lattice, known as phonons. They may also collide with one another. Frustratingly, a conventional temperature test warms the electrons and the lattice together, so the effects arrive tangled in the same resistance measurement.

Nickel disulfide, NiS₂, is an unusual material. Its interior behaves as an electrical insulator, blocking the flow of current, while certain parts of its surface conduct electricity freely. This contradiction has puzzled physicists for decades, and a recent study offers a detailed explanation. The conduction, it turns out, is confined to tiny one-dimensional steps on the surface, and these narrow conducting channels are a direct consequence of how electrons are arranged inside the crystal.

Mott insulator

NiS₂ shares its crystal structure with pyrite, the mineral sometimes called fool’s gold. At ordinary conditions, its electrons do not move freely through the lattice: the strong electrical repulsion between them opens an energy gap that keeps the bulk of the material insulating. This behaviour defines what physicists call a Mott, or charge-transfer, insulator, a category of materials that simple band theory cannot explain. Band theory predicts that any material with a partially filled outer electron shell should conduct electricity, yet compounds like nickel oxide obstinately insulate instead. In 1949, the physicist Nevill Mott showed why: if two electrons crowding the same atomic site cost more energy than is available, the electrons stay locked in place and no current flows, regardless of what band theory predicts. NiS₂ behaves in much the same way.

Yet electrical-transport measurements had repeatedly found that crystals of NiS₂ conduct through their surfaces. Earlier scanning-tunnelling experiments helped explain part of the puzzle: the broad, flat surface remains insulating, but the electronic gap narrows sharply near atomic-scale steps, tiny cliffs just one or two atoms high where the surface abruptly changes level. A new study ¹ confirms this picture and examines the steps with much higher spatial resolution than before.

A not that smooth surface

A scanning tunnelling microscope (STM) works by bringing an extremely sharp needle close enough to a surface that electrons can leak across the gap between tip and sample. Measuring that leakage at different energies reveals both the surface’s shape and how easily electrons can enter or leave it. In NiS₂, these measurements uncovered electronic states concentrated tightly along the step edges: the states extend for a long distance parallel to a step but stay confined to roughly one to two nanometres across it. In other words, the electrons are effectively free to move in one direction while remaining trapped in the other two, forming genuine one-dimensional conduction channels.

Two distinct kinds of surface step were observed, depending on whether the outermost atomic layer exposes nickel or sulfur atoms. Both carry electronic states associated with their steps, but they are not equally important. The nickel-terminated steps host states that sit right at the energy where electrical conduction happens, making them the most likely explanation for the surface conductivity that transport experiments had measured for years. The sulfur-terminated steps also host states inside the insulating gap, but their energy is positioned further away, making them less directly responsible for carrying current.

The study also tested what happens when a magnetic field is applied perpendicular to the surface. The step-edge states survived fields as strong as 10 tesla, a field far stronger than any produced by a laboratory magnet used for everyday purposes. Their intensity weakened somewhat, particularly on the sulfur-terminated steps, but the states were never destroyed. This robustness matters because NiS₂ already displays complicated magnetic behaviour of its own, which might easily have disrupted a more fragile conducting state.

The deeper explanation lies in how electrons are distributed inside the crystal. In an ordinary insulator, the occupied electronic states can usually be pictured as clouds centred on the atoms themselves. NiS₂ is different: calculations show that part of its electron density is naturally centred at special positions between atoms, specifically near the midpoints of pairs of sulfur atoms, where no atom actually sits. Physicists call these obstructed charge centres, and materials built around them belong to a class known as obstructed atomic insulators, a concept that grew out of a broader effort over the past decade to classify materials by the geometry, and not just the energy, of their electron states.

Not ordinary metallic defects

This arrangement is not a chemical accident; it is protected by the symmetry of the crystal. When the crystal is cut to form a surface, though, the special positions that hosted this electron density can no longer fit together the way they did in the bulk. At a step edge, this mismatch creates what is known as a filling anomaly: an imbalance in how the available electronic states can be occupied, which leaves behind a state inside the insulating gap, localized right at the edge. Calculations of artificial step structures reproduce the main features seen under the microscope, including this localization, supporting the idea that the conducting channels are not ordinary metallic defects caused by broken chemical bonds, but a direct consequence of the crystal’s underlying electronic geometry.

The study also settles a long-standing question about NiS₂’s magnetism at low temperature. Below about 39 kelvin, the nickel magnetic moments arrange themselves into a non-collinear antiferromagnetic pattern, with neighbouring moments pointing in different directions that largely cancel out. Below about 30 kelvin, they rearrange again into a state that produces a small but measurable net magnetization. New neutron-diffraction measurements support a revised model of this low-temperature arrangement, resolving a debate about the material’s magnetic ground state that had lasted for roughly fifty years.

Taken together, the results give NiS₂ a significance well beyond its peculiar conducting surface. The material shows that strong repulsion between electrons, magnetism, and the geometry of electronic states can coexist within a single crystal. Such geometric protection is normally associated with topological materials, in which certain electronic states are shielded from disorder or defects by the crystal’s symmetry. The new results suggest that this protection can survive even when strong interactions push a material into being an insulator, making NiS₂ a rare setting for studying how the quantum-mechanical arrangement of electrons decides where electricity is allowed to flow within an otherwise insulating crystal.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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Topological quantum materials combine unusual electronic states with properties such as magnetism or superconductivity, offering possibilities for future electronics and quantum technologies. Researchers at Tohoku University have now shown that changing the number of layers in a crystal can provide a systematic way to design topological magnets. The work is published in the Journal of the American Chemical Society.

Topological quantum materials combine unusual electronic states with properties such as magnetism or superconductivity, offering possibilities for future electronics and quantum technologies. Researchers at Tohoku University have now shown that changing the number of layers in a crystal can provide a systematic way to design topological magnets. The work is published in the Journal of the American Chemical Society.

Material properties such as sound insulation, resistance to extreme heat and thermal expansion originate from how the zillions of microscopic building blocks (nuclei and electrons) interact at equilibrium and respond to perturbations. Atoms are typically about one ten-billionth of a meter across, so there can be a lot of parts to keep track of—a task that is complicated at the quantum-mechanical level, where particles are neither here nor there until observed.

Material properties such as sound insulation, resistance to extreme heat and thermal expansion originate from how the zillions of microscopic building blocks (nuclei and electrons) interact at equilibrium and respond to perturbations. Atoms are typically about one ten-billionth of a meter across, so there can be a lot of parts to keep track of—a task that is complicated at the quantum-mechanical level, where particles are neither here nor there until observed.

Researchers at Nagoya University have built a graphene nanoribbon that can switch which way it twists using a natural solvent. Graphene nanoribbons are thin ribbon-shaped structures made of fused carbon rings. Twisted or helical versions of these ribbons show promise for advanced light and electronic devices. However, no graphene nanoribbon could switch that twist on demand, until now.

Scientists have worked out how to switch between a right-handed and left-handed twist (chirality) by changing the solvent around it. The discovery ¹ opens opportunities for new optical switches, chemical sensors, and spintronic components that adapt to changing environments.

Tomoyuki Ikai, lead author and professor at Nagoya University’s Graduate School of Engineering, is a polymer chemist inspired by natural helical structures such as DNA and proteins. Polymers are large molecules built from many small, repeating units linked together in a chain. Ikai had been working on ladder polymers, where each repeating unit is locked into place and cannot freely rotate around the bond connecting to its neighbor (unlike a typical flexible linear polymer).

In 2019, Ikai and his collaborators built the first rigid, helix-shaped polymer. In 2021, they perfected a chemical method to fuse these building blocks together without flaws. This method is what let them build the new graphene nanoribbon.

“We used the same fusion approach already used to make predictable helical ladder polymers. But instead of a stable building block, such as [6]helicene, we used [4]helicene, a 4-ring unit written off as too unstable to be useful,” Ikai said.

Soak, twist, repeat

These units are difficult to control on their own because they switch their chirality too fast to hold one handedness. The team’s method fuses these small, restless units into one long chain. Once joined, they found that a neighbor effect took hold: each unit’s twist began to match its neighbors, and long stretches of the ribbon settled into a single, shared spiral.

To lock it in one overall direction, the researchers dissolved the ribbon in a natural chiral liquid, a liquid made of molecules that come in two mirror-image versions. They tested six candidates before they found the right one: beta-pinene, a compound found in pine trees and citrus peel.

Because beta-pinene molecules can be arranged in left- and right-hand mirror-images, these two versions each push the ribbon toward the opposite spiral. This also changed the twist direction of light the ribbon gave off, a property called circularly polarized luminescence, and is the first graphene nanoribbon shown to switch its light this way.

The switching induced a remarkably high degree of helical bias, with almost all of the helicene units aligning in the same direction. The switching effect is strongest at –90°C and grows weaker as the temperature rises toward room temperature.

“For a long time, people saw [4]helicene as unsuitable for chiral materials, because it could not be controlled,” Ikai said. “In this paper, we show that once you link enough of these units together, the instability itself becomes the useful part.”

A chiral solvent’s nudge toward one handedness is usually very weak on its own. Here, the ribbon’s own structure, with each unit mechanically linked to its neighbors, amplifies that weak nudge into a strong, nearly one-handed result.

An adaptive material

The researchers point to several possible future uses: The switchable light could serve optical devices. The ribbon’s chemical sensitivity to beta-pinene suggests it may work as a chiral sensor, and a similar design could one day help detect hazardous or unstable chemicals. Because graphene conducts electricity well, the ribbon may also suit electronic sensors.

The molecule’s twisted shape connects to spintronics, a field that uses the spin of electrons rather than just their charge. Ikai noted that a right-handed or left-handed structure can, in principle, let electrons of one spin pass through more easily than the other, a property helical structures are known for in physics literature.

The current design only holds its twist while it stays in the chiral liquid. If the solvent is removed, the ribbon drifts back to a mixed, unstable state. Ikai’s next goal is a form of “chiral memory,” a way for the ribbon to lock in its twist even after the solvent is gone. This next step builds on memory techniques the researchers have explored in other helical systems and is now applied to graphene for the first time.

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Water droplets sliding across solid surfaces can acquire electric potentials of thousands of volts and thereby corrode non-conductive surfaces on metals when they discharge. That is the conclusion of researchers in Germany who say that the poorly-understood phenomenon warrants further investigation to help prevent corrosion of vulnerable outdoor equipment and cultural heritage sites.

Metal corrosion by water droplets is a serious economic and safety issue, and prevention begins with the proper understanding of the relevant processes. Conventional wisdom is that most corrosion is caused by a combination of physical abrasion by the motion of the droplets and chemical degradation from natural acids and anthropogenic pollutants in the water. The notion that electrochemistry might play a significant role in corrosion had not been seriously considered, says physical chemist Hans-Jürgen Butt of the Max Planck Institute for Polymer Research in Mainz.

Part of the reason, he believes, is that, until relatively recently, it was thought that the triboelectric effect (electrically charging objects by rubbing them together) did not work in liquids. “If you have a solid and you rub another insulating solid against it you get electron transfer – I think this has been known for more than 2500 years” he says. However, this relies on atomic-scale roughness of the surface to concentrate charge at specific points where bonds can be broken – and fluids cannot, by definition, be rough.

“If you take a water droplet and let it slide there is some mechanical force from surface tension, but that’s much too low,” says Butt. “There is no way you could generate enough energy locally to pick up an electron or to put an electron or an ion from the water onto the surface.” In the past 10 years, however, it has become increasingly clear that sliding droplets do become highly charged.

Sloping surfaces

In their present work Butt and colleagues deposited water droplets onto copper surfaces covered with 60 nm of Teflon.  When they dropped droplets straight onto the surface, they observed no corrosion. They then deposited droplets first onto a variety of other sloped insulating surfaces such as plant leaves, PVC construction boards and the perfluorooctadecyltrichlorosilane (PFOTS) hydrophobic coating often used on window glass. The droplets ran down these surfaces and then fell onto the Teflon-coated copper. After around 3000 droplet impacts, atomic force microscopy and confocal microscopy revealed evidence that the droplets had corroded both the coating and the underlying copper.

The researchers believe that the droplets become positively charged as they slide down the sloping surface. As they fall onto the coating, the potential difference between the copper and the underlying copper can exceed 1 kV. This is greater than the dielectric breakdown strength of the coating, causing the droplet to discharge. This damages the coating and leaves the underlying metal vulnerable to further oxidation.

To test their hypothesis, the researchers measured charge movement within the copper surface, showing that negative charge flowed towards droplets dripping off insulating surfaces. They also used high-speed cameras to show that, whereas a drop deposited directly retained its spherical shape before impact, a dripping drop was drawn into a cone shape, producing a tip of positive charge that would increase its corrosive capacity.

Uncertain consequences

The practical implications of this are unclear. “Technical coatings on cars, ships etc. are typically 100 microns and thicker, so the process we describe is probably not of direct relevance,”says Butt. However, the phenomenon could be involved in the degradation of monuments and other outdoor historical objects. “We have evidence that surfaces change their properties when you slide charges over them, but the real consequences are not yet known,” explains Butt.

He says his own group is most clearly focused on understanding the fundamental physics involved. “We still don’t know why the heck there is such a charge separation: it’s energetically unfavourable, it should not happen, but it happens.” he says. “The one effect we describe here is, in a way, pretty trivial – everyone knows that if you have a high potential and it’s somehow grounded there is a breakthrough – but what happens at the surface with this deposited charge is not clear.”

Materials scientist Zhong Lin Wang of Georgia Institute of Technology in Atlanta was one of the first researchers to discover the triboelectric effect in liquids, and helped to develop the triboelectric nanogenerator used to quantify it. “The transferred electrons can be kicked back to the water solution, resulting in chemical reaction at the vicinity surface. This process, called contact-electro-catalysis, was first proposed in 2022, and is now an active field of research in chemistry, materials and environmental science.” He says. “[Butt and colleagues] show that the electrons transferred from the water droplet can ‘break’ the surface coating layer and lead to local oxidation. This is an interesting discovery.”

The research is described in Nature.

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Fusion reactors, devices that generate energy by fusing light atomic nuclei at extremely high temperatures, could contribute to ongoing efforts aimed at producing electricity more sustainably. The extreme environment inside these devices, however, can damage materials that surround the superheated, electrically charged plasma where the nuclear fusion reaction takes place.

Every electronic and optoelectronic device generates heat, and today that heat is managed almost entirely from the outside. Heatsinks, fans, cold plates and refrigerators are bulky exterior measures bolted onto a chip or package after the fact. They treat heat as a single averaged quantity to be removed in bulk, even though the heat is actually produced locally, component by component, deep inside the circuitry.

In January 2024, physicists at TU Dortmund University demonstrated a continuous time crystal in a semiconductor whose oscillations remained stable for hours. In a new study published in Nature Communications, Professor Alex Greilich and his team show that many such time crystals can form in the same material and synchronize their electron-nuclear spin oscillations.

Over the last decade, researchers have developed two-dimensional materials with fascinating quantum effects that could be harnessed for next-generation technologies.

Scientists in China predict that stacking two microscopic layers of boron could set a new record for superconductivity. Superconductors are materials that conduct electricity with zero resistance. Traditional types need temperatures close to absolute zero to work, requiring complex and expensive cooling equipment.

A new mechanism governing the geometric shapes of growing elastic sheets has been identified by a trio of physicists in Israel. Through a combination of simulations and experiments, Eran Sharon and colleagues at the Hebrew University of Jerusalem showed that the dimpled patterns that form in a growing elastic object have topological origins.

This mechanism is unrelated to geometric incompatibilities, which are known to dimple natural materials. The discovery could lead to a deeper understanding of how complex shapes emerge in the natural world – and to the development of new artificial materials.

Thin sheets are ubiquitous in nature: examples include leaves, petals, and the cellular linings of organs and blood vessels. The complex makeup of natural sheets means that local regions within them have preferred mechanical rest states that are incompatible with those of other regions. As a result, there is no way to arrange the sheet so that every part is simultaneously stress free – leading to effects like wrinkling, bending, and buckling.

Called geometric incompatibility, this phenomenon is responsible for numerous geometric forms in the natural world, enabling growing tissues to shape themselves without any external influence. For some time, researchers have attempted to mimic these natural mechanisms in synthetic materials.

Richness of shapes

“Looking at natural growth processes, as in plants growth, or embryo development, we see amazing richness of shapes and shape development that currently cannot be achieved with conventional fabrication methods,” says Sharon.

Sharon’s group has already shown that many patterns in nature can be understood in terms of the Gauss and Mainardi-Codazzi-Peterson incompatibilities – which were developed in the 19^th century. Together with team member Michael Moshe, whose group explores the interplay between mechanics and geometry in soft materials, their work led to discoveries including the mechanical origins of shape selection in rose petals.

Now, Moshe and Sharon have teamed-up with Yafei Zhang to identify a phenomenon that cannot be explained by those mechanical instabilities. In their experiment, they started with a uniform elastic sheet formed into a hollow sphere, with circular holes at each pole. When they added wedges of material into the sheet to mimic growth, it initially behaved like a smooth, growing sphere – but only up to a certain point.

Missing mechanism

“The growing sheet satisfies the established local compatibility conditions, and is thus expected to show smooth ‘boring’ shape,” Moshe explains. “Yet it unexpectedly, develops a crumpled appearance, suggesting that an important shaping mechanism was missing from the existing framework.”

Important clues came when the team cut into the crumpled sphere along a meridian, from pole to pole. Instantly, the crumpling disappeared, and the sphere relaxed back to its original smooth shape. This effect also occurs in simulations of a smoothly growing sphere.

With no changes to the Gauss or Mainardi-Codazzi-Peterson incompatibilities governing the mechanical forces in the sheet, the trio concluded that the sudden transformation emerged from an entirely different mechanism, rooted in the mathematical principles of topology. In this view, unlike smooth geometric transformations such as bending, stretching, or twisting, which preserve a shape’s mechanical properties, cutting introduces a sudden transformation that changes its mechanical behaviour.

In this way, the meridional cut brought the sphere into a new topological state. “Unlike conventional incompatibility, this frustration is topological in character, and can be quantified by a global measure,” Moshe explains. “It provides a new mechanism by which growing sheets can select complex, wrinkled or dimpled shapes.”

The trio’s discovery now raises new mathematical questions about the limits of growing elastic sheets, beyond which their smooth geometries can no longer be maintained. “What we have discovered that the geometrical principles we knew before should be supplemented with topological considerations, leading to an even wider class of shaping principles,” Sharon says. “This allows a better understanding of morphogenetic processes and expands our abilities to shape synthetic structures.”

In turn, the team’s insights could uncover new understanding of how shaping mechanisms could be harnessed, perhaps leading to the discovery of new metamaterials, with shapes and mechanical functions programmed into their growth.

The research is described in Physical Review Letters.

The post Topology affects the crumpling of growing elastic sheets appeared first on Physics World.

Ruthenium dioxide (RuO2) is a metal oxide that commonly serves as an important metallic conductor, quantum material and industrial electrocatalyst. While there have been debates surrounding the magnetic properties of RuO2, it is generally thought to be nonmagnetic in its bulk form. But now, a new study, published in Science Advances, has found that very thin layers of RuO2 can become magnetic when its lattice is placed under strain.

One of the most striking discoveries in condensed matter physics over the past few years is that simply rotating one atomically thin crystal on top of an identical layer can create entirely new electronic behavior. This idea became famous in 2018, when physicists found that graphene sheets stacked at a very particular “magic angle” could turn into a superconductor, even though a single sheet of graphene is not. That discovery launched an entire field, sometimes called twistronics, built around moiré patterns: the large-scale interference patterns that appear when two crystal lattices are laid on top of each other with a slight mismatch in angle or spacing. In many materials, these patterns reshape how electrons move, sometimes producing superconductivity or other exotic collective states.

Moiré collapse

Most of this research has focused on materials whose crystal structure looks roughly the same in every direction, such as graphene, where the interesting physics shows up only at very small twist angles, close to perfect alignment. Now, a team of researchers instead looks at a strongly directional material: bilayer black phosphorus, whose atomic structure behaves very differently along two perpendicular directions in the plane, somewhat like a fabric that stretches easily one way but not the other. That built-in directionality turns out to change the whole logic of moiré physics, producing an effect the authors call moiré collapse. ¹

In black phosphorus, the two layers start out rotated 90 degrees relative to each other. As that angle is dialed away from 90 degrees, the moiré pattern does something unusual. Rather than staying a two-dimensional pattern, like a slowly shifting checkerboard, it stretches more and more along one direction until, at a specific angle that depends only on the material’s own geometry, it effectively stops repeating in the other direction altogether. What remains behaves like a one-dimensional crystal, even though the material is still built from ordinary two-dimensional atomic sheets. For twisted bilayer black phosphorus, the calculations place this collapse at a twist of about 71.6 degrees, or equivalently about 18.4 degrees away from the initial 90-degree arrangement.

Pure geometry

This transformation has nothing to do with how electrons repel or attract each other; it is pure geometry. The mathematical description of the moiré pattern, expressed in terms of the directions in which its periodicity repeats, is squeezed from two independent directions down to one. In ordinary space, this means the pattern keeps a well-defined repeat distance along one axis while stretching out indefinitely along the other, with no repeating pattern left in that direction at all.

Such a dramatic structural change reshapes the electrons riding on top of it. At the untwisted 90-degree configuration, the anisotropy of one layer happens to cancel out the anisotropy of the other, so electrons move about equally well in every in-plane direction. As the twist angle approaches the collapse point, that cancellation breaks down. The electron energy bands become sharply directional, and electrons increasingly travel along one preferred line rather than spreading across the plane. Their energy spectrum starts to show the telltale fingerprints of one-dimensional systems, including sharp spikes in the density of available electron states known as one-dimensional van Hove singularities.

Luttinger liquid physics

One-dimensional conductors behave very differently from ordinary metals. In a three-dimensional metal, electrons can mostly be treated as independent particles that only weakly notice one another. Confine them to a single dimension, however, and that picture stops working: electrons cannot slip past each other, so they are forced to move collectively, in a coordinated wave-like fashion. The framework that describes this collective behavior, called Luttinger liquid theory, traces back to work by Sin-Itiro Tomonaga in 1950 and Joaquin Luttinger in 1963, and it has since been confirmed experimentally in systems such as carbon nanotubes. In a Luttinger liquid, the basic excitations are not single electrons at all, but collective ripples of charge and spin, and this leads to electrical transport properties that look qualitatively different from those of a normal metal.

The calculations in this study show that moiré collapse naturally sets up the conditions Luttinger liquid physics requires. As the collapse angle is approached, the one-dimensional electronic channels that form become progressively less coupled to their neighbors, making the correlated, wave-like behavior increasingly favorable. The analysis estimates a Luttinger parameter of about 0.3 for the collapsed black phosphorus system, a value indicating strong electron-electron interactions, and it predicts distinctive collective charge oscillations and unusual, non-metallic patterns in electrical conduction that could, in principle, be measured in the laboratory.

A notable feature of this mechanism is that the electron bands stay quite dispersive even at collapse, with electron speeds exceeding 100 kilometers per second. This sets it apart from most previously studied moiré systems, including twisted graphene, where strong correlations usually arise because the electronic bands become extremely flat and electrons effectively slow to a crawl. Here, the correlated behavior instead comes from the geometric collapse of the moiré lattice itself, with fast-moving electrons confined to one dimension rather than slow ones spread over two.

Moiré collapse is not a peculiarity of one material

To test these ideas, the researchers combined simplified mathematical models with detailed first-principles calculations of the atomic and electronic structure. Beyond black phosphorus, they found the same collapse in twisted bilayer tin selenide, another layered material with strongly directional bonding. The details of the electronic structure differ somewhat because of the specific atomic orbitals involved, but the same geometric collapse into quasi-one-dimensional channels appears, suggesting the phenomenon is not a peculiarity of one material but a general consequence of twisting any sufficiently anisotropic crystal.

Taken together, the findings outline a different strategy for engineering exotic quantum matter. Instead of hunting for a special magic angle that flattens electronic bands, as in twisted graphene, this approach relies on a purely geometric collapse angle at which a two-dimensional moiré material naturally turns one-dimensional. If confirmed in experiments, it would offer a new and versatile platform for studying Luttinger liquids and other correlated electronic phases that only emerge when electrons are squeezed into moving along a single line.

 

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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