In conventional superconductors, Bardeen-Cooper-Schrieffer (BCS) theory describes how phonon vibrations bind electrons together into Cooper pairs. The material properties of these superconductors often conform to “Matthias’ rules” – no magnetism, no oxides, no insulators. Apart from sulfur hydrides, no BCS superconductors exceed temperatures of 40 K. None of this has prevented doped copper oxides, whose parent compounds are insulating antiferromagnets, from remaining superconducting at temperatures up to 135 K. The coppers superconductors are mostly insensitive to changes in phonon frequency. Copper superconductors vary in their chemical formulas, but they all contain the same basic building block: planes with a copper atom sandwiched between two oxygen atoms. There are many hypotheses about the mechanism behind the superconductivity of coppers. Some theorists have proposed spin fluctuations. others believe that phonons are the answer. Less than a year after the discovery of copper’s superconductivity by Georg Bednorz and Alex Müller, Philip Anderson proposed that the glue that binds electrons comes from superexchange, in which the spins of the copper atoms couple, creating a magnetic attraction between the electrons them than the non-magnetic oxygen atom. between. Recently, several studies have begun to link the key factors behind a possible hyperexchange coupling mechanism. An important factor is the charge transfer gap (CTG), the energy required (typically 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 remove an electron from the copper. Last year, theorists at the University of Sherbrooke in Quebec calculated the rate at which the electron pair varies with the CTG. This prediction provided a key target for a team led by JC Séamus Davis, who has laboratories at the University of Oxford, University College Cork in Ireland and Cornell University. In a recent study in the Proceedings of the National Academy of Sciences (PNAS), Davis and colleagues report evidence consistent with the Canadian theorists’ predictions, suggesting that the mechanism behind copper’s superconductivity is CTG-mediated superexchange .
Reconstruction models
Although BCS theory can be solved analytically—John Schrieffer famously solved the key equation for Cooper pairs in the metro—the theory behind high-Tc superconductors is more complicated. To simplify the picture, researchers often turned to a single-band Hubbard model in which copper 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 copper phase transitions occur. But the one-band Hubbard model does not account for multiple electron orbitals between copper and oxygen because it essentially crushes 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 these dynamics. At the same time, other theorists began to point to the importance of oxygen. Jeff Tallon, an experimenter at Victoria University of Wellington, New Zealand, suggested that there was a correlation between the oxygen hole content – the amount of electron holes present in an oxygen atom – and the maximum Tc. Deriving responses from three-band Hubbard models has remained elusive until recently. Since the early 1990s, new algorithms and exponential increases in computing power have allowed theorists to capture the dynamics of many more atoms and previously intractable problems involving magnetic impurities. With these tools, theorists at the University of Sherbrooke returned to the problem. Theorists began by trying to make sense of two experimental findings: that a large CTG correlates with low Tc and that low oxygen hole content correlates with low Tc. By solving the three-zone Hubbard model for the lattice, the Sherbrooke researchers demonstrated the connection between these results. They found that increasing CTG decreases the oxygen hole content by compressing the oxygen p orbitals, leaving less room for holes. A longer CTG also limits the strength of the hyperexchange interaction because it is a barrier to coupling. Putting everything together, the authors concluded that the electron pairing mechanism is hyperexchange, which in turn depends on the content of CTG and the oxygen hole. Sherbrooke’s theoretical paper, published last year in PNAS, “is a real milestone in the long journey to understand cuprates,” says Tallon. The authors also proposed an elegant explanation for why the coppers are special: Among all the transition metals, the strongest covalent bond exists between copper and oxygen. Strong covalent bonds lead to more superexchange than weak or ionic bonds. Crucially, the Sherbrooke theorists also identified a quantifiable goal for future experiments: They predicted how much a given change in CTG would affect the density of Cooper pairs. “From the experimenter’s point of view, now you have traction,” says Davis. “If the degree-of-freedom control can be measured and if the response can be measured, then you can do real physics.”
Laboratory work
To verify Sherbrooke’s prediction, Davis and co-workers chose the cuprate Bi2Sr2CaCu2O8+x (BSCCO, pronounced “bisco”) because of its unique periodic property. The height of the oxygen atom above the copper atom in BSCCO varies by up to 12%—a huge difference that shows up as wavy lines in the topography 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 through the local 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 the out-of-plane oxygen atoms (gray) lead to decreases in the charge transfer gap (green) and an increased density of Cooper pairs (orange). Credit: Wangping Ren & Shane O’Mahony Davis and co-workers used two very different scanning tunneling microscopy (STM) approaches to measure BSCCO at about 15% hole doping. To measure the electron pair, the probe tip must be within picometers of the surface of the flat, flake material, where the electric field is on the order of 109 V/m. (The Josephson STM technique that Davis used to measure took a decade to develop, he says.) To measure CTG, the detector must be 5,000 times farther away—like operating a record player with a stylus on the other side of a room, says Davis. He and his team had to split the experiment into two parts and perform the measurements with different STM tips. Correlating changes in CTG with differences in Cooper pair density allowed the researchers to demonstrate a strong and fascinating correlation, perhaps the clearest evidence yet of a mechanism underlying copper’s superconductivity. The Davis group’s paper is “an amazing tour de force,” says Tallon. But that doesn’t mean one of the biggest questions in condensed matter physics has been answered. “Is this the key experiment to identify the long-awaited microscopic origin of copper superconductivity?” he asks. “With all due respect to the authors, my view is not yet.” Inna Vishik, a condensed matter experimenter at the University of California, Davis, agrees. “It’s an association that suggests a mechanism, but ultimately, it motivates further experimental work in terms of evaluating this in other compounds,” says Vishik, who was not involved in the recent studies. The relationship between the charge transfer gap (left) and the density of Cooper pairs (right), illustrated in the wavy ripples of the BSCCO layers. Where the CTG is larger (light), the density of Cooper pairs is lower (dark). where the CTG is smaller (dark), the density of Cooper pairs is greater (light). Taken together, the two measurements depict a visible link suggesting CTG-mediated hyperexchange as a mechanism for electron pairing. Credit: Wangping Ren & Shane O’Mahony Another recent study, published in Nature Communications, points to superexchange as the mating mechanism in mercury-based coppers. “We were investigating 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 percent?” They found that the difference in magnetic energy exactly corresponded to the difference in Tc, suggesting a superexchange-like magnetic basis for the mechanism. One issue with any cuprate study is doping. Unlike impurities in semiconductors, whose quantities are known to within one part per million, oxygen is difficult and difficult to determine better than one part per 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 from superconductivity to the pseudogap phase, it would seriously compromise the authors’ conclusions. Davies argues that their sample was far from the pseudogap region, but acknowledges that the pseudogap remains mysterious. In addition, there are exceptions: Some copper superconductors, such as La2−xSrxCuO4, have large superexchange but…
