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.
More than 40 trillion gallons of rain drenched the Southeast United States in the last week from Hurricane Helene and a run-of-the-mill rainstorm that sloshed in ahead of it — an unheard of amount of water that has stunned experts.
That’s enough to fill the Dallas Cowboys’ stadium 51,000 times, or Lake Tahoe just once. If it was concentrated just on the state of North Carolina that much water would be 3.5 feet deep (more than 1 meter). It’s enough to fill more than 60 million Olympic-size swimming pools.
“That’s an astronomical amount of precipitation,” said Ed Clark, head of the National Oceanic and Atmospheric Administration’s National Water Center in Tuscaloosa, Alabama. “I have not seen something in my 25 years of working at the weather service that is this geographically large of an extent and the sheer volume of water that fell from the sky.”
The flood damage from the rain is apocalyptic, meteorologists said. More than 100 people are dead, according to officials.
Private meteorologist Ryan Maue, a former NOAA chief scientist, calculated the amount of rain, using precipitation measurements made in 2.5-mile-by-2.5 mile grids as measured by satellites and ground observations. He came up with 40 trillion gallons through Sunday for the eastern United States, with 20 trillion gallons of that hitting just Georgia, Tennessee, the Carolinas and Florida from Hurricane Helene.
Clark did the calculations independently and said the 40 trillion gallon figure (151 trillion liters) is about right and, if anything, conservative. Maue said maybe 1 to 2 trillion more gallons of rain had fallen, much if it in Virginia, since his calculations.
Clark, who spends much of his work on issues of shrinking western water supplies, said to put the amount of rain in perspective, it’s more than twice the combined amount of water stored by two key Colorado River basin reservoirs: Lake Powell and Lake Mead.
Several meteorologists said this was a combination of two, maybe three storm systems. Before Helene struck, rain had fallen heavily for days because a low pressure system had “cut off” from the jet stream — which moves weather systems along west to east — and stalled over the Southeast. That funneled plenty of warm water from the Gulf of Mexico. And a storm that fell just short of named status parked along North Carolina’s Atlantic coast, dumping as much as 20 inches of rain, said North Carolina state climatologist Kathie Dello.
Then add Helene, one of the largest storms in the last couple decades and one that held plenty of rain because it was young and moved fast before it hit the Appalachians, said University of Albany hurricane expert Kristen Corbosiero.
“It was not just a perfect storm, but it was a combination of multiple storms that that led to the enormous amount of rain,” Maue said. “That collected at high elevation, we’re talking 3,000 to 6000 feet. And when you drop trillions of gallons on a mountain, that has to go down.”
The fact that these storms hit the mountains made everything worse, and not just because of runoff. The interaction between the mountains and the storm systems wrings more moisture out of the air, Clark, Maue and Corbosiero said.
North Carolina weather officials said their top measurement total was 31.33 inches in the tiny town of Busick. Mount Mitchell also got more than 2 feet of rainfall.
Before 2017’s Hurricane Harvey, “I said to our colleagues, you know, I never thought in my career that we would measure rainfall in feet,” Clark said. “And after Harvey, Florence, the more isolated events in eastern Kentucky, portions of South Dakota. We’re seeing events year in and year out where we are measuring rainfall in feet.”
Storms are getting wetter as the climate change s, said Corbosiero and Dello. A basic law of physics says the air holds nearly 4% more moisture for every degree Fahrenheit warmer (7% for every degree Celsius) and the world has warmed more than 2 degrees (1.2 degrees Celsius) since pre-industrial times.
Corbosiero said meteorologists are vigorously debating how much of Helene is due to worsening climate change and how much is random.
For Dello, the “fingerprints of climate change” were clear.
“We’ve seen tropical storm impacts in western North Carolina. But these storms are wetter and these storms are warmer. And there would have been a time when a tropical storm would have been heading toward North Carolina and would have caused some rain and some damage, but not apocalyptic destruction. ”
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It’s a dinosaur that roamed Alberta’s badlands more than 70 million years ago, sporting a big, bumpy, bony head the size of a baby elephant.
On Wednesday, paleontologists near Grande Prairie pulled its 272-kilogram skull from the ground.
They call it “Big Sam.”
The adult Pachyrhinosaurus is the second plant-eating dinosaur to be unearthed from a dense bonebed belonging to a herd that died together on the edge of a valley that now sits 450 kilometres northwest of Edmonton.
It didn’t die alone.
“We have hundreds of juvenile bones in the bonebed, so we know that there are many babies and some adults among all of the big adults,” Emily Bamforth, a paleontologist with the nearby Philip J. Currie Dinosaur Museum, said in an interview on the way to the dig site.
She described the horned Pachyrhinosaurus as “the smaller, older cousin of the triceratops.”
“This species of dinosaur is endemic to the Grand Prairie area, so it’s found here and nowhere else in the world. They are … kind of about the size of an Indian elephant and a rhino,” she added.
The head alone, she said, is about the size of a baby elephant.
The discovery was a long time coming.
The bonebed was first discovered by a high school teacher out for a walk about 50 years ago. It took the teacher a decade to get anyone from southern Alberta to come to take a look.
“At the time, sort of in the ’70s and ’80s, paleontology in northern Alberta was virtually unknown,” said Bamforth.
When paleontogists eventually got to the site, Bamforth said, they learned “it’s actually one of the densest dinosaur bonebeds in North America.”
“It contains about 100 to 300 bones per square metre,” she said.
Paleontologists have been at the site sporadically ever since, combing through bones belonging to turtles, dinosaurs and lizards. Sixteen years ago, they discovered a large skull of an approximately 30-year-old Pachyrhinosaurus, which is now at the museum.
About a year ago, they found the second adult: Big Sam.
Bamforth said both dinosaurs are believed to have been the elders in the herd.
“Their distinguishing feature is that, instead of having a horn on their nose like a triceratops, they had this big, bony bump called a boss. And they have big, bony bumps over their eyes as well,” she said.
“It makes them look a little strange. It’s the one dinosaur that if you find it, it’s the only possible thing it can be.”
The genders of the two adults are unknown.
Bamforth said the extraction was difficult because Big Sam was intertwined in a cluster of about 300 other bones.
The skull was found upside down, “as if the animal was lying on its back,” but was well preserved, she said.
She said the excavation process involved putting plaster on the skull and wooden planks around if for stability. From there, it was lifted out — very carefully — with a crane, and was to be shipped on a trolley to the museum for study.
“I have extracted skulls in the past. This is probably the biggest one I’ve ever done though,” said Bamforth.
“It’s pretty exciting.”
This report by The Canadian Press was first published Sept. 25, 2024.
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.”
