Skip to Main Content
Skip Nav Destination

Cuprate superconductivity mechanism may be coming into focus

18 November 2022

Theory and experiment have pinpointed factors that determine the magnetic attraction between electron pairs.

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.

Relationship between oxygen height, charge-transfer gap, and density of 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.

Relationship between charge-transfer gap (left) and density of Cooper pairs (right).
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.

Close Modal

or Create an Account

Close Modal
Close Modal