condensed matter physics

Decoding the Secrets of Superconductivity

Experimentalists have pinpointed the microscopic structure of waves inside high-temperature superconductors, which could be the key to understanding the complex materials.

The microscopic structure of high-temperature superconductors has long puzzled scientists seeking to harness their virtually limitless technological potential. Now at last researchers have deciphered the cryptic structure of one class of the superconductors, providing a basis for theories about how they manage to transport electricity with perfect efficiency when cooled, and how scientists might raise their operating temperature closer to the climes of everyday life.

This goal, if realized, could make an array of fantastical-sounding technologies commercially viable, from power grids that never lose energy and cheap water purification systems to magnetically levitating vehicles. Scientists believe room-temperature superconductivity would have an impact on a par with that of the laser, a 1960 invention that now plays an important role in an estimated $7.5 trillion in economic activity.

“In the same way that a laser is a hell of a lot more powerful than a light bulb, room-temperature superconductivity would completely change how you transport electricity and enable new ways of using electricity,” said Louis Taillefer, a professor of physics at the University of Sherbrooke in Quebec.

Materials that superconduct under much warmer conditions than their ultra-cooled predecessors were discovered in 1986, winning IBM researchers Georg Bednorz and K. Alex Müller the Nobel Prize in physics soon after. But 28 years later, these “high-temperature” superconductors still fall short of room temperature by more than 100 degrees Celsius. The materials’ complexity has so far frustrated the dream of dialing up their operating temperatures. Researchers say the new findings are firmly setting them on the right track.

“If you want to cure a disease, first you have to discover that microbes exist. This is like discovering which microbes exist,” said J. C. Seamus Davis, a professor of physics at Cornell University and St. Andrews University and director of the Department of Energy’s Center for Emergent Superconductivity at Brookhaven National Laboratory.

The “microbes” in this case are ripples of electrons inside the superconductors that are called charge density waves. The fine-grained structure of the waves, reported in two new papers by independent groups of researchers, suggests that they may be driven by the same force as superconductivity. Davis and his colleagues directly visualized the waves in a study posted online in April, corroborating indirect evidence reported in February by a team led by Riccardo Comin, a postdoctoral fellow at the University of Toronto.

“It’s a beautiful paper,” said Dirk Morr, a professor of physics at the University of Illinois, Chicago, speaking of the work of Davis and his colleagues. “One can really trust this result and build our theories from it.”

Subir Sachdev, a professor of physics at Harvard University who helped devise Davis’ study, correctly predicted the form of the charge density waves in a paper last year, which detailed a possible mechanism behind both the waves and high-temperature superconductivity. Though further tests are needed, Sachdev’s theory is garnering support from many experts, who say it succinctly captures key features of the materials.

Taken together, the various findings are at last starting to build a comprehensive picture of the physics behind high-temperature superconductivity. “This is the first time I feel like we’re making real progress,” said Andrea Damascelli, a professor of physics at the University of British Columbia who led two recent studies on charge density waves. “A lot of different observations which have been made over decades did not make sense with each other, and now they do.”

The rate of progress in recent months has been “almost overwhelming for us,” Comin said. With better experimental tools at their disposal, he and other researchers described rushing to publish one interesting new result after another as fascinating papers by their competitors piled up on their desks.

“It’s been a roller coaster ride,” said Davis. “It’s been like 24 hours a day for weeks.”

The Face of the Enemy

High-temperature superconductivity seems like a miracle of quantum mechanics, one that could be harnessed to great effect if only it could be understood.

The property is exhibited primarily by cuprates, brittle ceramic materials composed of two-dimensional sheets of copper and oxygen separated by more complicated layers of atoms. When cuprates are cooled below a certain temperature, electrons in the copper-oxygen sheets suddenly overcome their mutual repulsion and pair up. With their powers combined, they behave like a different type of particle altogether, a boson, which has the unique ability to join with other bosons into a coherent swarm that moves as one. This bosonic swarm perfectly conducts electricity. A current flowing through a loop of cuprate wire will persist forever — or as long as the liquid-nitrogen fridge stays on.

“The biggest question in the field is, what force binds the electrons together?” Taillefer said. “Because if you can understand the force, you can strengthen the force.”

In “conventional” superconductivity, the kind exhibited by many metals when they are cooled near absolute zero (zero degrees on the Kelvin scale, or minus 273.15 degrees Celsius), electron pairing is caused by gentle pressure waves that breeze through the metals. When an electron gets swept along by one of these waves, another follows in its wake, attracted by the positively charged metal atoms that shift toward the passing electron. But this light breeze cannot possibly explain pairing in cuprates, which survives at up to 160 kelvins (minus 113 C). Many competing forces seem to influence the electrons simultaneously, and the force that binds them together over such a broad temperature range must be strong enough to overcome others that strive to keep them apart. The devil is in disentangling the forces. In the words of Pegor Aynajian, an assistant professor of physics at Binghamton University in New York, “It feels like we’re in a battlefield and we don’t know who’s our ally and who’s our enemy.”

The first sign of what looks increasingly like the enemy — charge density waves, also known as “charge order” — came in 2002. Using a new kind of microscope that could map currents on the surface of cuprates with nanometer resolution, Davis, then a professor at the University of California, Berkeley, and Jennifer Hoffman, his graduate student at the time, discovered a minute pattern of denser and less-dense ripples of electrons that appeared wherever they blasted the cuprate with a powerful magnetic field, an effect that suppressed superconductivity. Soon, other labs reported more actions that both killed superconductivity and produced the waves, such as raising the temperature or lowering the cuprates’ oxygen concentration.

“You start to build this picture in which charge density waves are lurking, waiting to take over when anything unfriendly to superconductivity happens,” said Hoffman, who is now an associate professor at Harvard.

It seemed possible that if the force shaping electrons into charge density waves could be suppressed, its rival, the force that forms superconducting pairs, would flourish. But some researchers argued that the ripples of electrons were merely a surface anomaly and irrelevant to superconductivity.

The community remained divided until 2012, when two groups using a technique called resonant X-ray scattering managed to detect charge density waves deep inside cuprates, cementing the importance of the waves. As the groups published their findings in Science and Nature Physics, two new collaborations formed, one led by Damascelli and the other by Ali Yazdani of Princeton University, with plans to characterize the waves even more thoroughly. Finishing in a dead heat, the rival groups’ independent studies appeared together in Science in January 2014. They confirmed that charge density waves are a ubiquitous phenomenon in cuprates and that they strenuously oppose superconductivity, prevailing as the temperature rises.

“Now we know this superconducting state has to fight for survival against this other state,” said Taillefer. “I don’t know how much that charge order hurts you. But boy, it’s time to find out.”

A D-Wave Pattern

To defeat the enemy on the superconductor battleground, scientists first needed to understand it. That required a closer look at the underlying structure of charge density waves. How do electrons, which are confined to the orbits of atoms, give rise to the waves that ripple through cuprates’ copper-oxygen layers?

Davis and his Cornell group have been steadily improving their microscope’s resolution over the years, and in 2007 they managed to detect variations in the distribution of electrons within cuprates’ smallest nooks and crannies: the “unit cells” that tile the materials’ copper-oxygen layers. Each cell consists of a central copper atom bonded to oxygen atoms at its northern and eastern edges. The scientists discovered that electrons are more likely to be found along the northern bond in some unit cells and the eastern bond in others. Davis suspected that this uneven distribution of electrons inside the cells, a form known as “d-wave,” was the root source of the charge density waves that appear to undulate across multiple unit cells. “But we just couldn’t close the deal,” he said.

Meanwhile at Harvard, Sachdev also wondered whether the d-wave arrangement of electrons observed in Davis’ 2007 work was the true microscopic structure of the charge density waves. On a Saturday afternoon in March of this year, Sachdev emailed Davis asking if he had been able to infer anything about the waves from his electron distribution data. Davis replied that he had long suspected that the two phenomena were connected, but that he couldn’t come up with the right algorithm for gleaning one from the other. Within an hour, Sachdev devised a procedure that he thought would do the trick and sent it over. Sure enough, by applying Sachdev’s algorithm to a new round of data, Davis and his group mapped out the structure of the charge density waves, showing that the d-wave distribution of electrons was, indeed, their source.

“The paper establishes that the two patterns are the same,” Sachdev said. “It just works beautifully.”

The results fully confirmed the earlier report by Damascelli, Comin and their co-authors, which used X-ray data to reveal the same d-wave form of the charge density waves. Although Damascelli’s group reached the milestone first, Davis says his team went further. “Basically they published indirect evidence for the same state as we have visualized directly,” he said.

The waves’ structure is particularly suggestive, researchers say, because superconducting pairs of electrons also have a d-wave configuration. It’s as if both arrangements of electrons were cast from the same mold. “Until a few months ago my thought was, OK, you have charge density waves, who cares? What’s the relevance to the high-temperature superconductivity?” Damascelli said. “This tells me these phenomena feed off the same interaction.”

Conjoined Twins

Many theorists believe both phenomena are caused by a quantum mechanical effect called antiferromagnetism, a tendency in some materials for neighboring electrons to spin in opposite directions. The effect sets up a chessboard pattern of electrons spinning upward and downward. Just as squares along diagonals on a chessboard have the same color, electrons positioned along 45-degree angles spin the same way.

Antiferromagnetism has long been considered one of the likeliest agents to be responsible for high-temperature superconductivity. Proponents of the idea argue that the force coupling electrons is essentially an attraction between oppositely spinning neighbors. This explains why the electron pairs always form along the cardinal directions in the crystal lattice but never along the diagonals — another d-wave arrangement. This well-known d-wave nature of superconductivity is slightly different from that of charge density waves. But in a theory that Sachdev and his collaborators have developed, “we find that the two d-waves are indeed linked to each other.”

In 2010, Sachdev and his student Max Metlitski showed mathematically that antiferromagnetism could cause pairing not only between electrons, but also between electrons and “holes,” or places in the orbits of atoms where electrons could exist but are missing. Electron-hole pairs are widely regarded as the basic building blocks of charge density waves, just as pairs of electrons are the building blocks of superconductivity. Furthermore, in July 2013, Sachdev and another student, Rolando La Placa, showed that the resulting electron-hole pairs would arrange themselves in a d-wave form — in this case, the kind observed in Davis’ recent experiment.

In short, antiferromagnetism could generate the d-wave patterns of both superconductivity and its rival, charge density waves.

“It makes sense that antiferromagnetism is the parent state of both charge density waves and superconductivity,” said Suchitra Sebastian, a physicist at Cambridge University whose own new work on charge density waves will appear soon in Nature. “Many key aspects we know so far are consistent with that, and it seems very likely to be the explanation of what is happening.”

Hoffman called Sachdev’s new framework a “beautiful descriptive theory.” But she pointed out that it is not yet refined enough to predict how the balance of charge density waves and superconductivity vary with temperature, magnetic field or type of cuprate. “The ultimate goal is of course a predictive theory which will allow new materials and new technology,” she said.

Other theories tying together antiferromagnetism, charge density waves and superconductivity remain in play, said Steve Kivelson, a theoretical physicist at Stanford University who has been arguing for 20 years that the three phenomena might be intertwined. The correct theory of their relationship is far from settled, Kivelson said, and the biggest advance has been on the experimental side: “I think probably the focus should be more on the experiment.”

Even if Sachdev’s theory (or some other) turns out to be correct, it remains to be seen whether materials scientists can find a way to significantly turn up the heat on superconductivity. It might simply be impossible. But in recent years, these scientists have proved remarkably successful at tweaking the knobs on nature’s raw materials. “They are usually miraculous at doing this,” Davis said.

Sachdev’s theory makes a suggestion. It indicates that the two types of pairs, electron-electron and electron-hole, are equally likely consequences of antiferromagnetism, so changing the strength of that interaction won’t help superconductivity dominate over charge density waves. But there are other differences between the pairs — for instance, electron-hole pairs move more sluggishly through the cuprate lattice — and altering a certain property of the material would kill off these slow movers. How to tweak this property is, Sachdev said, “obviously the question we are thinking about.”

Other researchers have their own ideas about how to increase the temperature range across which superconductivity dominates over charge density waves. Some refused to divulge their approaches. “The prize is so big,” said Hoffman, explaining the competitiveness of the field. “If somebody finds a room-temperature superconductor, that’s huge, in terms of personal fame, in terms of gifts to humanity, in terms of prestige and legacy.”

The biggest advantage of elevating superconductivity to room temperature would be accessibility. Just as the laser and computers unexpectedly yielded the Internet, many uses of superconductivity are probably still unknown. The point is to make the technology available and see what happens. “Right now there are a bunch of highly specialized guys in the lab fooling around with superconductivity,” Taillefer said. “That’s not what you want. You want the whole planet fooling around with superconductivity.”

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