Maddury Somayazulu, an experimental physicist who goes by Zulu, could only hope that being close would be good enough. In an equipment-crammed room at Argonne National Laboratory in Illinois, he was huddled with postdoctoral researcher Zachary Geballe over a plum-sized cylindrical gadget called a diamond anvil cell. Inside was a dust speck’s worth of the rare-earth metal lanthanum and a bit of hydrogen gas, which theorists had predicted could morph into a novel compound under the enormous pressure of 2.1 million atmospheres. That is more than half the pressure at the center of Earth and, more relevant on that June 2017 day, near the limits of the cell’s capacity to compress its contents between its two pebble-sized diamonds—among the hardest materials in nature. As the scientists turned the cell’s screws up to 1.7 million atmospheres, they felt them tighten. The diamonds, already warped by the pressure, could break. “Okay, that’s it. We can’t go any higher,” Somayazulu said. “Let’s try to synthesize here and see what happens.”
The scientists had surrounded the anvil cell with a kind of high-tech firing squad: two long tubes for bombarding it with x-rays, a constellation of lenses and mirrors for blasting it with a laser, and a video camera to record the assault. They hoped that once activated, the laser would catalyze the lanthanum-hydrogen reaction. Outside the room, behind a sliding metal door that shielded them from the x-rays, the scientists watched a computer screen showing a graph of the x-rays’ assessment of their mixture’s microscopic structure. The plot quickly assumed the desired shape. They had successfully crushed and blasted lanthanum hydride, or LaH10, into existence. “We were shocked,” Somayazulu says. “We didn’t even have to heat it much and it formed the compound”—and not just any compound.
Theory and computer modeling had suggested that LaH10 could be a superconductor, a material with the uncanny ability to conduct electricity without the energy losses that bedevil conventional wires. This efficiency allows a prodigious amount of current to be packed into a small space and circulate, perpetual-motion style, forever. Better yet, LaH10 was supposed to work this magic at about 44 degrees Fahrenheit (280 kelvins), a far higher temperature than achieved by any known superconductor and tantalizingly close to room temperature, a long-standing goal. The frigid conditions required by existing superconductors have tended to limit their use to niche applications such as MRI machines and particle accelerators. But a room-temperature superconductor might be put to many more uses, including transporting solar and wind energy to greater distances than currently practical, increasing the capacity of creaking power grids, making batteries that never lose their charge, and countless others in computers and medicine.
The x-ray analysis that Somayazulu and Geballe received indicated that the LaH10 they had created showed the exact microscopic structure theorists had predicted. “That hit us,” Somayazulu told me during a recent visit to Argonne, where he joined the staff in May. When he and his colleagues synthesized LaH10, he was still working for the Geophysical Laboratory of the Carnegie Institution for Science in Washington, D.C. His boss at the time, Russell Hemley, calls LaH10 “a beautiful example of materials by design.” Hemley led the team that created the compound, as well as the theoretical group that predicted its existence and its properties. “We built this material on a computer first, and a calculation told us where to look for it.”
That was the real novelty of LaH10. Scientists have searched for high-temperature superconductors for more than a century, but nearly every breakthrough has come from some combination of guesswork—essentially, trying out different ingredients and processes one by one, in hopes of success—and good luck. Only once before had a computer program prophesied a high-temperature superconductor—H3S, another high-pressure compound found in 2014 that also falls into the hydrogen-bearing class of “hydrides”—but even in that case its creators were actually trying to make something else. The diamond-breaking pressures required to keep hydrides intact make it highly unlikely that they will ever be useful, but the algorithms that anticipated them, along with other recent computational advances, have the potential to make the search for more practical superconductors more systematic, and possibly more fruitful, than ever before.
A Theory of Superconductivity
“LaH10 was really a godsend,” Somayazulu says, recounting the years of labor that led to the material’s discovery. Clearly excited as he recalls the tale, he sounds like he is still trying to believe he made it. He would still be out there, he says, “lost” and navigating the wilds with “rough ideas” and “high school chemistry,” were it not for the new algorithms and their predictions.
Even so, once LaH10 had been conjured, he still had to figure out how to test it for superconductivity. Ever since the phenomenon’s discovery in 1911, when Dutch physicist Heike Kamerlingh Onnes observed the electrical resistance of a mercury wire immersed in liquid helium inexplicably vanish at 4.2 kelvins, findings of new superconducting materials have tended to precede theories that explain them. Although superconductivity turns out to be surprisingly common, and many other elements have since been shown to superconduct (all below 10 kelvins), no one could begin to make sense of it until quantum mechanics was developed in the 1920s. The explanation depends on the electrons responsible for electricity behaving as both localized particles and spread-out waves, the way quantum mechanics says all subatomic particles do. On this basis, scientists John Bardeen, Leon N. Cooper and John Robert Schrieffer devised a theory now known as BCS (after their initials) to describe the physics of superconductors and published it in 1957.
It built on scientists’ basic understanding of current: Inside a metal, the atoms (actually, atomic nuclei plus some bound electrons, which create positively charged ions) form a crystal lattice—a structure with regular spacing—plus a sea of free electrons that, when a voltage is applied, flow through the lattice to form an electric current. Typically lattice imperfections and vibrations resulting from heat impede this flow and create resistance. According to BCS theory, however, electrons can foil this friction with a feat of quantum aikido that turns lattice motions to their advantage. First, as an electron moves through the lattice it bends the lattice’s atoms in its direction of travel (because of the attraction between its negative charge and the lattice’s positive charge). This bending bunches positive charges together, and the resulting concentration of positive charge pulls a second electron into the first’s wake, bonding the two into a so-called Cooper pair. Second, those pairs, acting more like waves than particles now, overlap, synchronize and coalesce into one big wave called a Bose-Einstein condensate that is too large to be impeded by the lattice and so flows through it without any resistance at all.
BCS theory has led to many successful predictions, including the so-called critical temperatures above which superconductors lose their superpowers. Nevertheless, it has generally been of little help in the search for new superconductors with higher critical temperatures. In fact, the most successful superconductor hunter in history was an experimentalist named Bernd Matthias who deemed BCS irrelevant to his pursuit. Matthias discovered hundreds of superconductors (many of which were metal alloys) between the 1950s and the 1970s by testing countless materials in his lab, guided largely by five empirical rules relating to material properties (for example, “high symmetry is good”) and one overarching principle: “Stay away from theorists.”
But despite Matthias’s many conquests, the highest critical temperature seen in a superconductor rose only slightly, from 17 to 23 kelvins, between 1955 and 1973. And there it stayed until 1986, when Georg Bednorz and Alex Müller, two IBM scientists in Zurich, discovered superconductivity in a class of complex layered ceramics called cuprates. These materials still hold the record for high temperature at ambient pressure that they set in 1993: 135 kelvins. Unlike Matthias, Bednorz and Müller “had a very robust theoretical view about what they were looking for,” says physicist Peter Littlewood of the University of Chicago. “Now those ideas are probably wrong.”
Wrong because they were based on BCS theory and the way it invokes atomic lattice vibrations, or phonons, to create Cooper pairs. Although such pairs, and the Bose-Einstein condensate they form, are believed to underlie the cuprates’ superconductivity, many experts today believe the Cooper bonds in cuprates depend on some form of direct electromagnetic interaction between the electrons instead of, or at least in addition to, phonons. Alas, those direct interactions are so difficult to model mathematically that more than three decades of intensive research have failed to yield an equivalent to BCS theory for the cuprates or even to create a consensus on the details of the electrons’ pairing mechanism. Scientists lump cuprates into a catchall category with several other classes of superconductors whose success seems to depend on various types of direct electron-to-electron interactions. These materials are called unconventional superconductors to distinguish them from the conventional, phonon-driven kind described by BCS.
So Bednorz and Müller found what they were looking for, but it did not work the way they thought it would. Yet that is superconductivity’s serendipitous way. For example, in 2006 scientists stumbled on iron-based superconductors—another unconventional class that lacks a theory to describe or predict it—while doing research to improve flat-panel displays. “Almost invariably, some new weird material is discovered,” Littlewood says, “and that then teaches us about a new mechanism [for electron pairing] that we hadn’t thought about.”
The Temperature Barrier
Superconductivity favors a chill, says Michael Norman, a materials scientist at Argonne, because “temperature is just bad” for sustaining wavelike quantum behavior at useful, macroscopic scales. The energy of heat tends to break up the bonds in Cooper pairs and disrupt the coordinated quantum state of a wavelike condensate.
The number of pairs in a condensate and the strength of the bonds holding them together provide a barrier to thermal disruption. A superconductor’s critical temperature represents the height of this barrier—above this point it cannot withstand the heat. (The high barriers of the cuprates, for example, are thought to result from the way their direct electron-to-electron interactions create stronger Cooper pair bonds than those that come from the indirect mechanism of phonons.)
And yet “I don’t think anybody now doubts that there is a possibility for a room-temperature superconductor at ambient pressure,” says Norman, partly because of the way new superconductors and pairing mechanisms keep cropping up. Even for conventional superconductors, there is “no fundamental limit” to critical temperature, says Igor Mazin, a physicist at the Naval Research Laboratory in Washington, D.C. Instead, he says, there is “a sort of statistical limit,” meaning that such materials are simply less likely to exist. Phonon-mediated pairing tends to be stronger in wobblier atomic lattices (a perfectly rigid lattice could not support conventional superconductivity, which requires the lattice to pull toward an electron). Therefore, the exceptionally robust pairing needed for high-temperature conventional superconductivity seems to demand a special type of crystal structure, analogous to the elaborate designs engineers employ in modern bridges to keep them sturdy despite their flexing with the wind.
So room-temperature superconductors, if they exist, are undoubtedly rare. Yet hope springs from the immensity of the searchable landscape: the approximately 100 stable elements in the periodic table could yield 4,950 combinations of two, 161,700 of three, and so on. Factor in choices of stoichiometry (the ratios of elements in a compound) and lattice structure, and the possibilities are endless. So how do scientists find the exceptional materials in that chemical haystack?
The Superconductor Dream
One morning in November 2017, Somayazulu was driving to work and racking his brain. The test to confirm LaH10’s superconductivity was not going well. It required replacement of a metal gasket in the diamond anvil cell with an insulating material to prevent a short circuit during measurement of the resistance. But for months the hydrogen gas had been leaking out of every design the team tried. “Every day we’d come in and discuss, and we’d try once more,” Somayazulu says. “It was very frustrating.”
Then, sitting in traffic on the D.C. Capital Beltway, he had an idea: “Why don’t we use a source of hydrogen that is solid?” Somayazulu thought that ammonia borane, a hydrogen-rich substance he knew of from earlier research, just might release hydrogen in the right way. After several months of refinement, the design worked. He saw LaH10’s resistance plummet at 265 kelvins. He quickly snapped a picture with his phone, and then the team’s computer program crashed and the cell’s diamonds disintegrated. The photograph was all that was left of their feat, and it would be another six months before they could repeat it.
Somayazulu had spent nearly a quarter of a century trying to compress hydrogen into a superconductor. This was a dream Hemley had been chasing for decades, based on a prediction first made by physicist Neil Ashcroft of Cornell University in 1968. It could take as much as 10 million atmospheres of pressure to achieve such a material, Ashcroft acknowledged in 1983, but he theorized that a second element added to hydrogen might reduce that requirement by acting like a wedge to break up the H2 molecules that hydrogen is prone to form. Thus freed, the hydrogen atoms could vibrate in ways conducive to high-temperature superconductivity: the pliable bonds between them would promote strong phonon coupling between electrons, and their low atomic mass would foster phonons that vibrated at an unusually high frequency (and therefore high energy), which would attract electrons in large numbers to the condensate.
For years after arriving from India in 1994 to work with Hemley as a postdoctoral fellow at the Carnegie Institution, Somayazulu dutifully crushed and heated myriad hydrogen mixtures in various ways, finding plenty of interesting physics but no superconductivity. “Here I am trying to dope hydrogen systematically with all kinds of things,” he says. “I’m squeezing it to higher and higher pressures, and nothing is happening, and I’m kind of thinking, ‘Was Ashcroft wrong?’”
Ashcroft, in fact, was right, but it took the help of a new class of “structure search” computer programs to prove it. The programs seek viable compounds by virtually moving atoms around in search of a stable crystal structure, which, by the second law of thermodynamics, is that with the lowest capacity to lose energy as heat. Some programs use an evolutionary search approach that starts with a group of crystal structures, mashes them up, selects the fittest of the offspring to breed, then repeats the process until the best of the bunch is found. Scientists then apply BCS to evaluate that structure’s potential for superconductivity and to estimate its critical temperature.
In 2012 a group in China led by Yanming Ma used one such program to predict, in line with Ashcroft’s ideas, that calcium hydride (CaH6) could be made at pressures created by diamond anvil cells and would superconduct at a high temperature. Hemley and his team were soon crushing calcium into hydrogen, and they were not alone.
In 2014 a group led by Mikhail Eremets in Germany, following up on another of Ma’s predictions—that hydrogen sulfide (H2S), the noxious gas that rotten eggs emit, would superconduct at 80 kelvins under sufficient pressure—squeezed the smelly gas in a diamond anvil cell and saw, to the team members’ surprise, that it superconducted at 203 kelvins instead. Eremets had chanced on another superconducting compound, H3S, which held the high-temperature record before the synthesis of LaH10.
Hemley’s quest had become a race. In 2017, with help from a postdoc named Hanyu Liu from Ma’s group, he used a structure-search algorithm to predict LaH10 and gave his group the marching orders that led to that compound’s synthesis. Eremets soon made it, too; he confirmed the telltale resistivity drop, and, most recently, put it through a more comprehensive battery of tests to confirm its compatibility with BCS theory. It passed.
These discoveries combine elements of design with surprise. LaH10, for example, grew out of Hemley’s suggestion that Liu focus on compounds with the most hydrogen possible, to best approximate Ashcroft’s original idea. On the other hand, LaH10 is believed to derive its high-temperature performance in part from the vibrational modes of its special clathrate structure, in which hydrogen atoms enclose a lanthanum atom in a “cage”—a configuration that theorists “would have never guessed,” says Eva Zurek, a chemist who carries out structure searches at the University of Buffalo. But whether by design or surprise, the new programs have made theorists such as Ma and Zurek suddenly more relevant to the superconductor search. “I think experimentalists are taking us a lot more seriously than in the past,” Zurek says.
That theorists expedited the discovery of H3S and LaH10, conventional superconductors to which BCS theory applies, is one thing. What is more surprising is that they might do the same for unconventional superconductors, for which physicists have no working theory at all.
LaH10, in fact, was not the only big superconductivity story of 2018. The other was the discovery of the phenomenon in twisted bilayer graphene. Graphene is a single-atom-thick sheet of carbon atoms arranged in a hexagonal lattice. Twisted bilayer graphene consists of two such sheets, one on top of the other, with their lattices rotated by an angle. Despite its low critical temperature of 1.7 kelvins, this material has uncommonly strong Cooper pair bonds. Its simple structure involving a single element has inspired hope that it can be understood theoretically and that it might elucidate unconventional superconductivity in general. The discovery straddles the line between serendipity and computer foresight—“It’s half and half,” says Pablo Jarillo-Herrero, head of the group at the Massachusetts Institute of Technology behind the finding. The material superconducts only at a specific “magic” twist angle of 1.1 degrees, a value that first popped out of a computer model. Yet although theorists correctly predicted that this angle would produce a spike in electron–electron interactions, they did not guess that it would lead to superconductivity. That surprise was uncovered in the lab.
Still, the find highlights the potential of what Norman calls design principles: calculable qualities that can help predict superconductivity even in the absence of a comprehensive theory. Matthias’s first five rules were such principles, but exceptions to each ultimately arose in work with unconventional superconductors. Norman, however, pointed out in a 2016 paper that even unconventional superconductors of different classes display suggestive similarities, including many features of their phase diagrams, which are plots that show how their properties change with variables such as pressure and temperature. He also noted that layered, quasi-two-dimensional structures such as the cuprates seem to support high critical temperatures and that certain crystal structures appear to be advantageous. As more classes of superconductors turn up, he reasoned, more design principles should become apparent. And even now, with more than 12,000 known superconducting materials catalogued and characterized, it is reasonable to wonder whether there are useful yet undiscovered design principles lurking in the existing data.
Machine-learning algorithms are computer programs that modify themselves as they receive more data. Last year one such algorithm, trained on a database of thousands of materials, developed the ability to identify superconductors (conventional and unconventional) in another data set with 92 percent accuracy and to estimate their critical temperatures. Furthermore, it did so using only simple elemental properties such as atomic weight and melting temperature. But “it’s not the fact that the machine-learning algorithm can do it,” says the study’s lead author, Valentin Stanev of the University of Maryland. “The interesting part is how it is doing it. The insight is really which predictors the machine is using.”
Stanev pointed out that the most important design principle the algorithm found for the cuprates’ critical temperatures is a parameter (related to the numbers of electrons in the outermost orbits of the compound’s atoms) that, to his knowledge, no one had noticed before. The hope is that as more such predictors are identified they can be applied in aggregate to accelerate the search for new and better superconductors.
Instead of relying on luck in the lab, says Stefano Curtarolo, Stanev’s co-author and a materials scientist at Duke University, “machine learning will suggest a subset of compounds to try. Experimentalists, instead of testing 10 compounds and taking one year in the lab, are going to test 10,000 compounds on the computer and take only a few weeks.”
A Black Art
Although theorists have begun to predict new and interesting compounds, they are a long way from giving step-by-step instructions for making them in the lab. “There is something you do which works,” Somayazulu says, describing the process of material synthesis. “And you just keep doing exactly the same thing to make it work, and why you do it you have no idea.” It took him six months to repeat the LaH10 superconductivity test, for example, because the researchers were still debugging their protocol for making the compound. But at least they could create LaH10, which is not the case for CaH6, a compound that Ma’s search predicted in 2012 but that still evades all attempts to synthesize it. And yttrium? Don’t even get Somayazulu started on yttrium. Yttrium hydride (YH10) is supposed to superconduct at even higher temperatures than LaH10, but its behavior in Somayazulu’s experiments was just “horrible.” His ammonia borane trick, for example, does not work with it. Nor did it work with selenium at high pressure, although it did at low pressures. And recall how Eremets chanced on H3S when shooting for H2S. Clearly, materials synthesis is still very much a black art.
Structure search, meanwhile, entails its own difficulties. “The algorithms themselves you can just click a button,” Zurek says. “But the analyses can be tricky, and I wouldn’t want to have a nonexpert doing it,” she adds with a chuckle. It takes a supercomputer about a week, on average, to complete a search for a given stoichiometry and pressure, and many such combinations may be of interest for a given pair of elements. The heavy computation load, as well as the trickiness of analysis, restricts most searches to compounds of just two elements and not too many atoms in a unit cell, the fundamental building block of a crystal. “We still cannot reliably predict a system that has three elements and 50 atoms in a unit cell,” Zurek says.
Machine-learning programs, for their part, need not be so computationally intensive. Stanev ran his on a laptop. Their big limitation, and that of design principles generally, is that they can only leverage lessons learnable from known superconductors, which makes them unlikely to uncover a completely new class.
As for LaH10 and the other hydrides, their likely legacy depends on whom you ask. Hemley, who recently moved to the University of Illinois at Chicago, hopes that they hold lessons for creating an “analog” material able to maintain its high-temperature superconducting mojo at ambient pressure. Littlewood sees no reason for that to be impossible. Others are skeptical, though, because of pressure’s pivotal role in the hydrides’ performance so far. “You can afford to have strong electron–phonon coupling without destroying your crystal,” Mazin says, “because it’s being held together by external pressure.”
If such an analog is possible, it probably consists of at least three elements, Zurek says, and has a complex crystal structure, according to Mazin. More generally, the arc of higher-temperature superconductors seems to bend toward more complex materials. Single-element superconductors with single-digit critical temperatures were surpassed by Matthias’s metal alloys, which were outdone by materials with more elements and more complicated crystal structures. If, as many experts believe, the best hope for the room-temperature dream is an as yet unknown class of superconductors, then it seems likely to lie deep in the periodic table’s endless frontier.
Somayazulu, for one, is happy to have dispensed with Matthi-as’s rule against theorists. At Argonne, he spoke passionately about the failed attempts to make CaH6: the struggles in trying to produce it and the debates with theorists he had along the way. Sometimes the theorists taught the experimentalists something. Other times it was the reverse. For Somayazulu, that was the most important legacy of the hydrides: this new “feedback loop” between experiment and theory. “Every time the theory guys make a prediction, there’s a 50–50 chance it will work,” he says. “But at least now there’s that 50 percent chance.