Since their dramatic debut in 1986, cuprate superconductors have been some of the best-studied materials in existence. Nonetheless, many mysteries about the materials have persisted, including perhaps the key question: What mechanism compels electrons to overcome their repulsion and pair up?
In conventional superconductors, Bardeen-Cooper-Schrieffer (BCS) theory describes how phonon vibrations coax electrons together into Cooper pairs. The material properties of those superconductors often abide by “Matthias’s rules”—no magnetism, no oxides, no insulators. Apart from sulfur hydrides, no BCS superconductor exceeds temperatures of 40 K. None of that has stopped doped copper oxides, whose parent compounds are insulating antiferromagnets, from remaining superconducting at temperatures as high as 135 K. As further evidence against a BCS pairing mechanism, cuprate superconductors are mostly insensitive to changes in phonon frequency.
Cuprate superconductors vary in their chemical formulas, but all contain the same essential building block: planes with one copper atom sandwiched between two oxygen atoms. Hypotheses abound for the mechanism behind cuprates’ superconductivity. Some theorists have suggested spin fluctuations; others believe phonons are the answer. Less than a year after Georg Bednorz and Alex Müller’s discovery of cuprate superconductivity, Philip Anderson proposed that the glue that binds electrons comes from superexchange, in which the spins of copper atoms are coupled, creating a magnetic attraction among their electrons despite the nonmagnetic oxygen atom in between.
Recently, several studies have begun to connect the key factors behind a potential superexchange pairing mechanism. One important factor is the charge-transfer gap (CTG), the energy required (usually a few eV) for an oxygen atom to take an electron from a copper atom. The larger the gap, which exists between the copper d orbital and the oxygen p orbital, the less likely the oxygen is to nab an electron from the copper. Last year, theorists at the University of Sherbrooke in Québec computed the rate at which electron pairing varies with the CTG.
That prediction provided a key target for a team led by J. C. Séamus Davis, who has labs at Oxford University, University College Cork in Ireland, and Cornell University. In a recent study in Proceedings of the National Academy of Sciences (PNAS), Davis and his colleagues report evidence that agrees with the Canadian theorists’ predictions, suggesting the mechanism behind cuprate superconductivity is CTG-mediated superexchange.
Re-cuperating models
Although BCS theory can be solved analytically—John Schrieffer famously solved the key equation for the Cooper pairs on the subway—the theory behind high-Tc superconductors is more complex. To simplify the picture, researchers have often turned to a one-band Hubbard model in which the cuprate is approximated as a square lattice of spins. Anderson was able to use the model to show how superexchange might work; others have even used it to predict where cuprate phase transitions take place. But the one-band Hubbard model does not consider multiple electron orbitals between copper and oxygen because it essentially smashes the oxygen and copper into one effective molecule.
As early as 1989, Vic Emery at Brookhaven National Laboratory introduced a more realistic three-band Hubbard model to address those dynamics. At the same time, other theorists were beginning to point to oxygen’s importance. Jeff Tallon, an experimentalist at Victoria University of Wellington, New Zealand, proposed that there was a correlation between oxygen hole content—the amount of electron holes present on an oxygen atom—and maximum Tc.
Extracting answers from three-band Hubbard models has remained out of reach until recently. Since the early 1990s, new algorithms and exponential increases in computing power have allowed theorists to capture the dynamics of far more atoms and previously intractable problems about magnetic impurities. With those tools, the University of Sherbrooke theorists returned to the problem.
The theorists began by trying to understand two experimental findings: that a large CTG is correlated with low Tc and that low oxygen hole content is correlated with low Tc. By solving the three-band Hubbard model for the lattice, the Sherbrooke researchers demonstrated the connection between those results. They found that increasing the CTG lowers oxygen hole content by compressing oxygen p orbitals, leaving less room for holes. A larger CTG also limits the strength of the superexchange interaction because it presents a barrier to coupling. Putting everything together, the authors concluded that the electron pairing mechanism is superexchange, which in turn depends on the CTG and oxygen hole content.
The Sherbrooke theory paper, published last year in PNAS, “is a true landmark in the long journey to understand the cuprates,” Tallon says. The authors also suggested an elegant explanation for why cuprates are special: Among all the transition metals, the strongest covalent bond exists between copper and oxygen. Strong covalent bonds lead to more superexchange than do weak ones or ionic bonds.
Critically, the Sherbrooke theorists also identified a quantifiable target for future experiments: They predicted how much a given change to the CTG would affect the density of Cooper pairs. “From the experimentalist’s point of view, now you have traction,” says Davis. “If the controlling degree of freedom can be measured, and if the response can be measured, then you can do real physics.”
Laboratory labors
To verify the Sherbrooke prediction, Davis and his colleagues chose the cuprate Bi2Sr2CaCu2O8+x (BSCCO, pronounced “bisco”) because of its unique periodic property. The height of the oxygen atom located above the copper atom in BSCCO varies by up to 12%—a huge difference that appears as wavy lines in topographic imaging of the sample. According to the Sherbrooke theorists, increasing the oxygen height would decrease the CTG, and a smaller CTG would lead to a larger superexchange interaction, which is measurable via the local density of the Cooper pairs.
Top graph: Oxygen atoms (red dots) vary in height above copper atoms (blue dots). Bottom graphs: Measurements reveal that changes in the height of out-of-plane oxygen atoms (gray) lead to decreases in the charge-transfer gap (green) and increased density of Cooper pairs (orange). Credit: Wangping Ren & Shane O’Mahony
Davis and colleagues used two very different scanning tunneling microscopy (STM) approaches to measure BSCCO at about 15% hole doping. To measure the electron pair, the tip of the probe must come to within picometers of the surface of the flat, flaky material, where the electric field is on the order of 109 V/m. (The Josephson STM technique that Davis used for the measurement took a decade to develop, he says.) To measure the CTG, the probe must be 5000 times farther away—like operating a record player with a stylus on the other side of a room, Davis says. He and his team had to split the experiment into two parts and perform the measurements with different STM tips.
Matching changes in the CTG to differences in Cooper pair density allowed the researchers to demonstrate a strong and compelling correlation, perhaps the clearest evidence yet of a mechanism that underlies cuprate superconductivity.
The Davis group’s paper is “a stunning tour de force,” Tallon says. But that doesn’t mean that one of the biggest questions in condensed-matter physics has been answered. “Is this the clinching experiment for identifying the long-sought microscopic origins of cuprate superconductivity?” he asks. “With deep respect for the authors, my view is—not yet.”
Inna Vishik, a condensed-matter experimentalist at the University of California, Davis, agrees. “It’s a correlation which proposes a mechanism, but ultimately, it motivates further experimental work in terms of assessing this in other compounds,” says Vishik, who was not involved in the recent studies.
The relationship between the charge-transfer gap (left) and density of Cooper pairs (right), visualized in the wavy undulations of BSCCO layers. Where the CTG is largest (light), the density of Cooper pairs is lowest (dark); where the CTG is smallest (dark), the density of Cooper pairs is highest (light). Adjoined, the two measurements depict a visible link that suggests CTG-mediated superexchange as the mechanism for electron pairing. Credit: Wangping Ren & Shane O’Mahony
Another recent study, published in Nature Communications, points to superexchange as the pairing mechanism in mercury-based cuprates. “We were looking at these two systems with a 30% difference in Tc,” says lead author Yuan Li of Peking University. “The question we wanted to answer is very simple: Is the magnetic energy scale also different between these two by 30%?” They found the difference in magnetic energy corresponded exactly to the difference in Tc, suggesting a magnetic basis such as superexchange for the mechanism.
One issue with any cuprate study is doping. Unlike the dopants in semiconductors, whose amounts are known within a part per million, oxygen is tricky and hard to pin down to better than one part in a hundred. Differences in doping can have large effects on the electronic structure, even pushing the compound into the pseudogap region, making it neither an antiferromagnet nor a superconductor. If even part of the BSCCO crystals slipped out of superconductivity into the pseudogap phase, it would severely compromise the authors’ conclusions. Davis argues that their sample was far from the pseudogap region but acknowledges that the pseudogap remains mysterious.
Additionally, there are exceptions: Some cuprate superconductors, such as La2−xSrxCuO4, have a large superexchange but a low Tc. Performing measurements of those compounds could be extremely difficult because they lack BSCCO’s extreme reaction to changes in the CTG, a property that makes the material easier to measure. For now, Davis says he will focus on repeating the experiment on BSCCO under different conditions, especially doping. He hopes that in the future, theorists will predict more testable parameters that are soft targets for experimentalists. “Even if what we report is not correct, opening the door to measuring the correct degrees of freedom in a falsifiable way is the correct way forward in a complicated field like this,” he says.
Far from the adrenaline-fueled early days of high-Tc superconductors, the latest efforts are the culmination of steady, normal science. André-Marie Tremblay, an author on the Sherbrooke group’s paper, credits programs like the Canadian Institute for Advanced Research for continued support even after the honeymoon phase of cuprate superconductors was over. After all, many mysteries remain.
“Even if we are correct, in 30 years people will still say that the theory is not understood,” Tremblay says.
TEL AVIV, Israel (AP) — A rare Bronze-Era jar accidentally smashed by a 4-year-old visiting a museum was back on display Wednesday after restoration experts were able to carefully piece the artifact back together.
Last month, a family from northern Israel was visiting the museum when their youngest son tipped over the jar, which smashed into pieces.
Alex Geller, the boy’s father, said his son — the youngest of three — is exceptionally curious, and that the moment he heard the crash, “please let that not be my child” was the first thought that raced through his head.
The jar has been on display at the Hecht Museum in Haifa for 35 years. It was one of the only containers of its size and from that period still complete when it was discovered.
The Bronze Age jar is one of many artifacts exhibited out in the open, part of the Hecht Museum’s vision of letting visitors explore history without glass barriers, said Inbal Rivlin, the director of the museum, which is associated with Haifa University in northern Israel.
It was likely used to hold wine or oil, and dates back to between 2200 and 1500 B.C.
Rivlin and the museum decided to turn the moment, which captured international attention, into a teaching moment, inviting the Geller family back for a special visit and hands-on activity to illustrate the restoration process.
Rivlin added that the incident provided a welcome distraction from the ongoing war in Gaza. “Well, he’s just a kid. So I think that somehow it touches the heart of the people in Israel and around the world,“ said Rivlin.
Roee Shafir, a restoration expert at the museum, said the repairs would be fairly simple, as the pieces were from a single, complete jar. Archaeologists often face the more daunting task of sifting through piles of shards from multiple objects and trying to piece them together.
Experts used 3D technology, hi-resolution videos, and special glue to painstakingly reconstruct the large jar.
Less than two weeks after it broke, the jar went back on display at the museum. The gluing process left small hairline cracks, and a few pieces are missing, but the jar’s impressive size remains.
The only noticeable difference in the exhibit was a new sign reading “please don’t touch.”
VICTORIA – The British Columbia government is partnering with a bear welfare group to reduce the number of bears being euthanized in the province.
Nicholas Scapillati, executive director of Grizzly Bear Foundation, said Monday that it comes after months-long discussions with the province on how to protect bears, with the goal to give the animals a “better and second chance at life in the wild.”
Scapillati said what’s exciting about the project is that the government is open to working with outside experts and the public.
“So, they’ll be working through Indigenous knowledge and scientific understanding, bringing in the latest techniques and training expertise from leading experts,” he said in an interview.
B.C. government data show conservation officers destroyed 603 black bears and 23 grizzly bears in 2023, while 154 black bears were killed by officers in the first six months of this year.
Scapillati said the group will publish a report with recommendations by next spring, while an independent oversight committee will be set up to review all bear encounters with conservation officers to provide advice to the government.
Environment Minister George Heyman said in a statement that they are looking for new ways to ensure conservation officers “have the trust of the communities they serve,” and the panel will make recommendations to enhance officer training and improve policies.
Lesley Fox, with the wildlife protection group The Fur-Bearers, said they’ve been calling for such a committee for decades.
“This move demonstrates the government is listening,” said Fox. “I suspect, because of the impending election, their listening skills are potentially a little sharper than they normally are.”
Fox said the partnership came from “a place of long frustration” as provincial conservation officers kill more than 500 black bears every year on average, and the public is “no longer tolerating this kind of approach.”
“I think that the conservation officer service and the B.C. government are aware they need to change, and certainly the public has been asking for it,” said Fox.
Fox said there’s a lot of optimism about the new partnership, but, as with any government, there will likely be a lot of red tape to get through.
“I think speed is going to be important, whether or not the committee has the ability to make change and make change relatively quickly without having to study an issue to death, ” said Fox.
This report by The Canadian Press was first published Sept. 9, 2024.
The European Space Agency is fast-tracking a new mission called Ramses, which will fly to near-Earth asteroid 99942 Apophis and join the space rock in 2029 when it comes very close to our planet — closer even than the region where geosynchronous satellites sit.
Ramses is short for Rapid Apophis Mission for Space Safety and, as its name suggests, is the next phase in humanity’s efforts to learn more about near-Earth asteroids (NEOs) and how we might deflect them should one ever be discovered on a collision course with planet Earth.
In order to launch in time to rendezvous with Apophis in February 2029, scientists at the European Space Agency have been given permission to start planning Ramses even before the multinational space agency officially adopts the mission. The sanctioning and appropriation of funding for the Ramses mission will hopefully take place at ESA’s Ministerial Council meeting (involving representatives from each of ESA’s member states) in November of 2025. To arrive at Apophis in February 2029, launch would have to take place in April 2028, the agency says.
This is a big deal because large asteroids don’t come this close to Earth very often. It is thus scientifically precious that, on April 13, 2029, Apophis will pass within 19,794 miles (31,860 kilometers) of Earth. For comparison, geosynchronous orbit is 22,236 miles (35,786 km) above Earth’s surface. Such close fly-bys by asteroids hundreds of meters across (Apophis is about 1,230 feet, or 375 meters, across) only occur on average once every 5,000 to 10,000 years. Miss this one, and we’ve got a long time to wait for the next.
When Apophis was discovered in 2004, it was for a short time the most dangerous asteroid known, being classified as having the potential to impact with Earth possibly in 2029, 2036, or 2068. Should an asteroid of its size strike Earth, it could gouge out a crater several kilometers across and devastate a country with shock waves, flash heating and earth tremors. If it crashed down in the ocean, it could send a towering tsunami to devastate coastlines in multiple countries.
Over time, as our knowledge of Apophis’ orbit became more refined, however, the risk of impact greatly went down. Radar observations of the asteroid in March of 2021 reduced the uncertainty in Apophis’ orbit from hundreds of kilometers to just a few kilometers, finally removing any lingering worries about an impact — at least for the next 100 years. (Beyond 100 years, asteroid orbits can become too unpredictable to plot with any accuracy, but there’s currently no suggestion that an impact will occur after 100 years.) So, Earth is expected to be perfectly safe in 2029 when Apophis comes through. Still, scientists want to see how Apophis responds by coming so close to Earth and entering our planet’s gravitational field.
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“There is still so much we have yet to learn about asteroids but, until now, we have had to travel deep into the solar system to study them and perform experiments ourselves to interact with their surface,” said Patrick Michel, who is the Director of Research at CNRS at Observatoire de la Côte d’Azur in Nice, France, in a statement. “Nature is bringing one to us and conducting the experiment itself. All we need to do is watch as Apophis is stretched and squeezed by strong tidal forces that may trigger landslides and other disturbances and reveal new material from beneath the surface.”
The Goldstone radar’s imagery of asteroid 99942 Apophis as it made its closest approach to Earth, in March 2021. (Image credit: NASA/JPL–Caltech/NSF/AUI/GBO)
By arriving at Apophis before the asteroid’s close encounter with Earth, and sticking with it throughout the flyby and beyond, Ramses will be in prime position to conduct before-and-after surveys to see how Apophis reacts to Earth. By looking for disturbances Earth’s gravitational tidal forces trigger on the asteroid’s surface, Ramses will be able to learn about Apophis’ internal structure, density, porosity and composition, all of which are characteristics that we would need to first understand before considering how best to deflect a similar asteroid were one ever found to be on a collision course with our world.
Besides assisting in protecting Earth, learning about Apophis will give scientists further insights into how similar asteroids formed in the early solar system, and, in the process, how planets (including Earth) formed out of the same material.
One way we already know Earth will affect Apophis is by changing its orbit. Currently, Apophis is categorized as an Aten-type asteroid, which is what we call the class of near-Earth objects that have a shorter orbit around the sun than Earth does. Apophis currently gets as far as 0.92 astronomical units (137.6 million km, or 85.5 million miles) from the sun. However, our planet will give Apophis a gravitational nudge that will enlarge its orbit to 1.1 astronomical units (164.6 million km, or 102 million miles), such that its orbital period becomes longer than Earth’s.
It will then be classed as an Apollo-type asteroid.
Ramses won’t be alone in tracking Apophis. NASA has repurposed their OSIRIS-REx mission, which returned a sample from another near-Earth asteroid, 101955 Bennu, in 2023. However, the spacecraft, renamed OSIRIS-APEX (Apophis Explorer), won’t arrive at the asteroid until April 23, 2029, ten days after the close encounter with Earth. OSIRIS-APEX will initially perform a flyby of Apophis at a distance of about 2,500 miles (4,000 km) from the object, then return in June that year to settle into orbit around Apophis for an 18-month mission.
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Furthermore, the European Space Agency still plans on launching its Hera spacecraft in October 2024 to follow-up on the DART mission to the double asteroid Didymos and Dimorphos. DART impacted the latter in a test of kinetic impactor capabilities for potentially changing a hazardous asteroid’s orbit around our planet. Hera will survey the binary asteroid system and observe the crater made by DART’s sacrifice to gain a better understanding of Dimorphos’ structure and composition post-impact, so that we can place the results in context.
The more near-Earth asteroids like Dimorphos and Apophis that we study, the greater that context becomes. Perhaps, one day, the understanding that we have gained from these missions will indeed save our planet.
