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Physicists trap electrons in a 3D crystal

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Physicists trap electrons in a 3D crystal


Electrons move through a conducting material like commuters at the height of Manhattan rush hour. The charged particles may jostle and bump against each other, but for the most part they’re unconcerned with other electrons as they hurtle forward, each with their own energy.

But when a material’s electrons are trapped together, they can settle into the exact same energy state and start to behave as one. This collective, zombie-like state is what’s known in physics as an electronic “flat band,” and scientists predict that when electrons are in this state they can start to feel the quantum effects of other electrons and act in coordinated, quantum ways. Then, exotic behavior such as superconductivity and unique forms of magnetism may emerge.

Now, physicists at MIT have successfully trapped electrons in a pure crystal. It is the first time that scientists have achieved an electronic flat band in a three-dimensional material. With some chemical manipulation, the researchers also showed they could transform the crystal into a superconductor — a material that conducts electricity with zero resistance.

The electrons’ trapped state is possible thanks to the crystal’s atomic geometry. The crystal, which the physicists synthesized, has an arrangement of atoms that resembles the woven patterns in “kagome,” the Japanese art of basket-weaving. In this specific geometry, the researchers found that rather than jumping between atoms, electrons were “caged,” and settled into the same band of energy.

The researchers say that this flat-band state can be realized with virtually any combination of atoms — as long as they are arranged in this kagome-inspired 3D geometry. The results, appearing in Nature, provide a new way for scientists to explore rare electronic states in three-dimensional materials. These materials might someday be optimized to enable ultraefficient power lines, supercomputing quantum bits, and faster, smarter electronic devices.

“Now that we know we can make a flat band from this geometry, we have a big motivation to study other structures that might have other new physics that could be a platform for new technologies,” says study author Joseph Checkelsky, associate professor of physics.

Checkelsky’s MIT co-authors include graduate students Joshua Wakefield, Mingu Kang, and Paul Neves, and postdoc Dongjin Oh, who are co-lead authors; graduate students Tej Lamichhane and Alan Chen; postdocs Shiang Fang and Frank Zhao; undergraduate Ryan Tigue; associate professor of nuclear science and engineering Mingda Li; and associate professor of physics Riccardo Comin, who collaborated with Checkelsky to direct the study; along with collaborators at multiple other laboratories and institutions.


Setting a 3D trap

In recent years, physicists have successfully trapped electrons and confirmed their electronic flat-band state in two-dimensional materials. But scientists have found that electrons that are trapped in two dimensions can easily escape out the third, making flat-band states difficult to maintain in 2D.

In their new study, Checkelsky, Comin, and their colleagues looked to realize flat bands in 3D materials, such that electrons would be trapped in all three dimensions and any exotic electronic states could be more stably maintained. They had an idea that kagome patterns might play a role.

In previous work, the team observed trapped electrons in a two-dimensional lattice of atoms that resembled some kagome designs. When the atoms were arranged in a pattern of interconnected, corner-sharing triangles, electrons were confined within the hexagonal space between triangles, rather than hopping across the lattice. But, like others, the researchers found that the electrons could escape up and out of the lattice, through the third dimension.

The team wondered: Could a 3D configuration of similar lattices work to box in the electrons? They looked for an answer in databases of material structures and came across a certain geometric configuration of atoms, classified generally as a pyrochlore — a type of mineral with a highly symmetric atomic geometry. The pychlore’s 3D structure of atoms formed a repeating pattern of cubes, the face of each cube resembling a kagome-like lattice. They found that, in theory, this geometry could effectively trap electrons within each cube.

Rocky landings

To test this hypothesis, the researchers synthesized a pyrochlore crystal in the lab.


“It’s not dissimilar to how nature makes crystals,” Checkelsky explains. “We put certain elements together — in this case, calcium and nickel — melt them at very high temperatures, cool them down, and the atoms on their own will arrange into this crystalline, kagome-like configuration.”

They then looked to measure the energy of individual electrons in the crystal, to see if they indeed fell into the same flat band of energy. To do so, researchers typically carry out photoemission experiments, in which they shine a single photon of light onto a sample, that in turn kicks out a single electron. A detector can then precisely measure the energy of that individual electron.

Scientists have used photoemission to confirm flat-band states in various 2D materials. Because of their physically flat, two-dimensional nature, these materials are relatively straightforward to measure using standard laser light. But for 3D materials, the task is more challenging.

“For this experiment, you typically require a very flat surface,” Comin explains. “But if you look at the surface of these 3D materials, they are like the Rocky Mountains, with a very corrugated landscape. Experiments on these materials are very challenging, and that is part of the reason no one has demonstrated that they host trapped electrons.”

The team cleared this hurdle with angle-resolved photoemission spectroscopy (ARPES), an ultrafocused beam of light that is able to target specific locations across an uneven 3D surface and measure the individual electron energies at those locations.

“It’s like landing a helicopter on very small pads, all across this rocky landscape,” Comin says.

With ARPES, the team measured the energies of thousands of electrons across a synthesized crystal sample in about half an hour. They found that, overwhelmingly, the electrons in the crystal exhibited the exact same energy, confirming the 3D material’s flat-band state.

To see whether they could manipulate the coordinated electrons into some exotic electronic state, the researchers synthesized the same crystal geometry, this time with atoms of rhodium and ruthenium instead of nickel. On paper, the researchers calculated that this chemical swap should shift the electrons’ flat band to zero energy — a state that automatically leads to superconductivity.

And indeed, they found that when they synthesized a new crystal, with a slightly different combination of elements, in the same kagome-like 3D geometry, the crystal’s electrons exhibited a flat band, this time at superconducting states.

“This presents a new paradigm to think about how to find new and interesting quantum materials,” Comin says. “We showed that, with this special ingredient of this atomic arrangement that can trap electrons, we always find these flat bands. It’s not just a lucky strike. From this point on, the challenge is to optimize to achieve the promise of flat-band materials, potentially to sustain superconductivity at higher temperatures.”



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Early dark energy could resolve cosmology’s two biggest puzzles

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Physicists trap electrons in a 3D crystal


A new study by MIT physicists proposes that a mysterious force known as early dark energy could solve two of the biggest puzzles in cosmology and fill in some major gaps in our understanding of how the early universe evolved.

One puzzle in question is the “Hubble tension,” which refers to a mismatch in measurements of how fast the universe is expanding. The other involves observations of numerous early, bright galaxies that existed at a time when the early universe should have been much less populated.

Now, the MIT team has found that both puzzles could be resolved if the early universe had one extra, fleeting ingredient: early dark energy. Dark energy is an unknown form of energy that physicists suspect is driving the expansion of the universe today. Early dark energy is a similar, hypothetical phenomenon that may have made only a brief appearance, influencing the expansion of the universe in its first moments before disappearing entirely.

Some physicists have suspected that early dark energy could be the key to solving the Hubble tension, as the mysterious force could accelerate the early expansion of the universe by an amount that would resolve the measurement mismatch.

The MIT researchers have now found that early dark energy could also explain the baffling number of bright galaxies that astronomers have observed in the early universe. In their new study, reported in the Monthly Notices of the Royal Astronomical Society, the team modeled the formation of galaxies in the universe’s first few hundred million years. When they incorporated a dark energy component only in that earliest sliver of time, they found the number of galaxies that arose from the primordial environment bloomed to fit astronomers’ observations.

You have these two looming open-ended puzzles,” says study co-author Rohan Naidu, a postdoc in MIT’s Kavli Institute for Astrophysics and Space Research. “We find that in fact, early dark energy is a very elegant and sparse solution to two of the most pressing problems in cosmology.”

The study’s co-authors include lead author and Kavli postdoc Xuejian (Jacob) Shen, and MIT professor of physics Mark Vogelsberger, along with Michael Boylan-Kolchin at the University of Texas at Austin, and Sandro Tacchella at the University of Cambridge.

Big city lights

Based on standard cosmological and galaxy formation models, the universe should have taken its time spinning up the first galaxies. It would have taken billions of years for primordial gas to coalesce into galaxies as large and bright as the Milky Way.

But in 2023, NASA’s James Webb Space Telescope (JWST) made a startling observation. With an ability to peer farther back in time than any observatory to date, the telescope uncovered a surprising number of bright galaxies as large as the modern Milky Way within the first 500 million years, when the universe was just 3 percent of its current age.

“The bright galaxies that JWST saw would be like seeing a clustering of lights around big cities, whereas theory predicts something like the light around more rural settings like Yellowstone National Park,” Shen says. “And we don’t expect that clustering of light so early on.”

For physicists, the observations imply that there is either something fundamentally wrong with the physics underlying the models or a missing ingredient in the early universe that scientists have not accounted for. The MIT team explored the possibility of the latter, and whether the missing ingredient might be early dark energy.

Physicists have proposed that early dark energy is a sort of antigravitational force that is turned on only at very early times. This force would counteract gravity’s inward pull and accelerate the early expansion of the universe, in a way that would resolve the mismatch in measurements. Early dark energy, therefore, is considered the most likely solution to the Hubble tension.

Galaxy skeleton

The MIT team explored whether early dark energy could also be the key to explaining the unexpected population of large, bright galaxies detected by JWST. In their new study, the physicists considered how early dark energy might affect the early structure of the universe that gave rise to the first galaxies. They focused on the formation of dark matter halos — regions of space where gravity happens to be stronger, and where matter begins to accumulate.

“We believe that dark matter halos are the invisible skeleton of the universe,” Shen explains. “Dark matter structures form first, and then galaxies form within these structures. So, we expect the number of bright galaxies should be proportional to the number of big dark matter halos.”

The team developed an empirical framework for early galaxy formation, which predicts the number, luminosity, and size of galaxies that should form in the early universe, given some measures of “cosmological parameters.” Cosmological parameters are the basic ingredients, or mathematical terms, that describe the evolution of the universe.

Physicists have determined that there are at least six main cosmological parameters, one of which is the Hubble constant — a term that describes the universe’s rate of expansion. Other parameters describe density fluctuations in the primordial soup, immediately after the Big Bang, from which dark matter halos eventually form.

The MIT team reasoned that if early dark energy affects the universe’s early expansion rate, in a way that resolves the Hubble tension, then it could affect the balance of the other cosmological parameters, in a way that might increase the number of bright galaxies that appear at early times. To test their theory, they incorporated a model of early dark energy (the same one that happens to resolve the Hubble tension) into an empirical galaxy formation framework to see how the earliest dark matter structures evolve and give rise to the first galaxies.

“What we show is, the skeletal structure of the early universe is altered in a subtle way where the amplitude of fluctuations goes up, and you get bigger halos, and brighter galaxies that are in place at earlier times, more so than in our more vanilla models,” Naidu says. “It means things were more abundant, and more clustered in the early universe.”

“A priori, I would not have expected the abundance of JWST’s early bright galaxies to have anything to do with early dark energy, but their observation that EDE pushes cosmological parameters in a direction that boosts the early-galaxy abundance is interesting,” says Marc Kamionkowski, professor of theoretical physics at Johns Hopkins University, who was not involved with the study. “I think more work will need to be done to establish a link between early galaxies and EDE, but regardless of how things turn out, it’s a clever — and hopefully ultimately fruitful — thing to try.”

We demonstrated the potential of early dark energy as a unified solution to the two major issues faced by cosmology. This might be an evidence for its existence if the observational findings of JWST get further consolidated,” Vogelsberger concludes. “In the future, we can incorporate this into large cosmological simulations to see what detailed predictions we get.”

This research was supported, in part, by NASA and the National Science Foundation.



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Plant-derived secondary organic aerosols can act as mediators of plant-plant interactions

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A new study published in Science reveals that plant-derived secondary organic aerosols (SOAs) can act as mediators of plant-plant interactions. This research was conducted through the cooperation of chemical ecologists, plant ecophysiologists and atmospheric physicists at the University of Eastern Finland.

It is well known that plants release volatile organic compounds (VOCs) into the atmosphere when damaged by herbivores. These VOCs play a crucial role in plant-plant interactions, whereby undamaged plants may detect warning signals from their damaged neighbours and prepare their defences. “Reactive plant VOCs undergo oxidative chemical reactions, resulting in the formation of secondary organic aerosols (SOAs). We wondered whether the ecological functions mediated by VOCs persist after they are oxidated to form SOAs,” said Dr. Hao Yu, formerly a PhD student at UEF, but now at the University of Bern.

The study showed that Scots pine seedlings, when damaged by large pine weevils, release VOCs that activate defences in nearby plants of the same species. Interestingly, the biological activity persisted after VOCs were oxidized to form SOAs. The results indicated that the elemental composition and quantity of SOAs likely determines their biological functions.

“A key novelty of the study is the finding that plants adopt subtly different defence strategies when receiving signals as VOCs or as SOAs, yet they exhibit similar degrees of resistance to herbivore feeding,” said Professor James Blande, head of the Environmental Ecology Research Group. This observation opens up the possibility that plants have sophisticated sensing systems that enable them to tailor their defences to information derived from different types of chemical cue.

“Considering the formation rate of SOAs from their precursor VOCs, their longer lifetime compared to VOCs, and the atmospheric air mass transport, we expect that the ecologically effective distance for interactions mediated by SOAs is longer than that for plant interactions mediated by VOCs,” said Professor Annele Virtanen, head of the Aerosol Physics Research Group. This could be interpreted as plants being able to detect cues representing close versus distant threats from herbivores.

The study is expected to open up a whole new complex research area to environmental ecologists and their collaborators, which could lead to new insights on the chemical cues structuring interactions between plants.



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Folded or cut, this lithium-sulfur battery keeps going

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Physicists trap electrons in a 3D crystal


Most rechargeable batteries that power portable devices, such as toys, handheld vacuums and e-bikes, use lithium-ion technology. But these batteries can have short lifetimes and may catch fire when damaged. To address stability and safety issues, researchers reporting in ACS Energy Letters have designed a lithium-sulfur (Li-S) battery that features an improved iron sulfide cathode. One prototype remains highly stable over 300 charge-discharge cycles, and another provides power even after being folded or cut.

Sulfur has been suggested as a material for lithium-ion batteries because of its low cost and potential to hold more energy than lithium-metal oxides and other materials used in traditional ion-based versions. To make Li-S batteries stable at high temperatures, researchers have previously proposed using a carbonate-based electrolyte to separate the two electrodes (an iron sulfide cathode and a lithium metal-containing anode). However, as the sulfide in the cathode dissolves into the electrolyte, it forms an impenetrable precipitate, causing the cell to quickly lose capacity. Liping Wang and colleagues wondered if they could add a layer between the cathode and electrolyte to reduce this corrosion without reducing functionality and rechargeability.

The team coated iron sulfide cathodes in different polymers and found in initial electrochemical performance tests that polyacrylic acid (PAA) performed best, retaining the electrode’s discharge capacity after 300 charge-discharge cycles. Next, the researchers incorporated a PAA-coated iron sulfide cathode into a prototype battery design, which also included a carbonate-based electrolyte, a lithium metal foil as an ion source, and a graphite-based anode. They produced and then tested both pouch cell and coin cell battery prototypes.

After more than 100 charge-discharge cycles, Wang and colleagues observed no substantial capacity decay in the pouch cell. Additional experiments showed that the pouch cell still worked after being folded and cut in half. The coin cell retained 72% of its capacity after 300 charge-discharge cycles. They next applied the polymer coating to cathodes made from other metals, creating lithium-molybdenum and lithium-vanadium batteries. These cells also had stable capacity over 300 charge-discharge cycles. Overall, the results indicate that coated cathodes could produce not only safer Li-S batteries with long lifespans, but also efficient batteries with other metal sulfides, according to Wang’s team.

The authors acknowledge funding from the National Natural Science Foundation of China; the Natural Science Foundation of Sichuan, China; and the Beijing National Laboratory for Condensed Matter Physics.



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