If two sheets of graphene are stacked with a precise offset of 1.1° and cooled to 1.7 K, something stunning happens: The resistivity drops to zero. That observation of superconductivity, published in Nature concurrently with a session at the 2018 American Physical Society March Meeting, set off a flurry of excitement reminiscent of the “Woodstock of Physics”—the March 1987 APS event when high-temperature cuprate superconductors debuted.
Now, five years after the discovery of superconductivity in twisted bilayer graphene, experimentalists and theorists are still trying to unravel the mechanism behind the phenomenon. Recent demonstrations of superconductivity in three-, four- and even five-layer graphene raise intriguing new possible explanations. All the while, researchers are attempting to improve their techniques for assembling the finicky stacks of carbon.
“The thing I see that’s healthy about [the field] is that there are good questions to crack, but then every few months there seem to be some new results,” says Ali Yazdani, a condensed-matter experimentalist at Princeton University. In March dozens of researchers gathered at the Aspen Center for Physics in Colorado to discuss the latest work in the new field, which seems to have settled on a name: moiré quantum matter.
A surprising discovery
Not long after Andre Geim and Konstantin Novoselov isolated a single layer of graphene in 2004, theorists were already wondering about the properties of two layers, twisted at a small relative angle to create the kind of moiré pattern often seen naturally in graphite. (The term moiré was originally used to describe the pattern formed when two imperfectly aligned sheets of silk were pressed together.) A few years later, a team led by Eva Andrei, an experimentalist at Rutgers University, used scanning tunneling spectroscopy to observe that the electronic band structure of bilayer graphene appeared to depend on its twist. At angles near 1º, the researchers found flat bands—a band structure in which electrons are effectively isolated from one another, allowing other interactions such as magnetism to take precedence. In 2011 Allan MacDonald and Rafi Bistritzer, both then at the University of Texas at Austin, dubbed that the “magic angle”—although they did not predict it would lead to superconductivity.
“I did not know we were going to find superconductivity,” says Pablo Jarillo-Herrero, a condensed-matter experimentalist at MIT who led the 2018 study. He and his team didn’t expect it even after they observed twisted bilayer graphene acting like a correlated insulator, a state with properties strongly dependent on temperature that is a precursor to superconductivity in materials such as cuprates. “My students and I joked, … ‘Can you imagine if we dope it and we see superconductivity?’ ”
Jarillo-Herrero and his colleagues did, of course, observe superconductivity in magic-angle graphene. Furthermore, it seemed to be unconventional—that is, not the result of traditional electron–phonon pairing found in Bardeen-Cooper-Schrieffer (BCS) superconductors. In addition to the insulating phase’s adjacency to its superconducting phase, magic-angle graphene had a critical temperature far higher than the density of its paired electrons would suggest. “Someone told me, ‘If this is a conventional superconductor, it’s the most unconventional conventional superconductor,’” Jarillo-Herrero says.
The how remains elusive
The mechanism behind the superconductivity in magic-angle graphene remains unknown, although the consensus is that it is not BCS superconductivity. Recent studies by Yazdani, Jarillo-Herrero, and others have found that the superconducting behavior persists even though the thermal energy required to break apart paired electrons is extremely low.
Efthimios Kaxiras, a condensed-matter theorist at Harvard University, points to the idea that skyrmions—a kind of quasiparticle formed from twisted magnetic fields—could induce superconductivity by forming Cooper pairs themselves, rather than the electrons as in a typical BCS superconductor. He also has a hunch that phonons help mediate pairing, even if they are not a dominant mechanism as in BCS superconductors. “There’s a lot of interesting ideas and excitement,” he says. “I don’t think it’s settled.”
Raquel Queiroz, a condensed-matter theorist at Columbia University who specializes in topological quantum matter, raises the possibility that the geometry of the band structure influences its mechanism of superconductivity. But given the numerous confounding effects, proof of a topological connection remains out of reach.
The picture of magic-angle graphene has also gotten more complex with the addition of more layers. Stacking three layers of graphene, each offset by about 1.5°, results in a system that superconducts at about 2.5 K. Similarly, quadrilayer and pentalayer graphene stacks superconduct when twisted at specific angles. Twisted graphene “is not one superconductor,” says Jarillo-Herrero. “It is a family of superconductors.” Those multilayer graphene stacks seem to differ from their bilayer counterparts. Some exhibit far stronger superconductivity, whereas others with alternating twist angles don’t superconduct at all. As the system grows in layers, it grows in complexity. “It’s a moiré of a moiré of a moiré,” says Kaxiras. Each layer is correlated with the other layers, which makes the problem recursively complex.
In 2021 Yazdani’s group observed that when the bottom layer of bilayer magic-angle graphene was aligned with the atoms in its typical substrate, boron nitride, it lost its superconductivity because the symmetry of the bilayer graphene was broken. “You look at other moiré systems, which don’t have the symmetry—we haven’t yet found another superconductor,” Yazdani says. But the role of symmetry remains murky. Predictions based on symmetry suggest that bilayer graphene should be similar to quadrilayer graphene, with its even number of layers; instead, it has more in common with trilayer and pentalayer graphene.
Assembly challenges and promise
So far, assembly methods have not advanced at the frenetic pace of the discoveries. Experimentalists still use the labor-intensive method of mechanically exfoliating graphene flakes because they require much higher quality than is currently possible through chemical synthesis. The trouble, according to Dmitri Efetov, a condensed-matter experimentalist at the Ludwig-Maximilian University of Munich, is in layering the graphene, regardless of how it is produced. Device fabrication remains something of an art: Even the most experienced groups successfully create superconducting devices only about half the time, and less experienced labs may have a success rate lower than 10%.
Quality outweighs quantity when it comes to producing samples for analysis. “I still think that if we make the samples better, this very system will show other physics,” Yazdani says. He points to researchers studying the fractional quantum Hall effect, the phenomenon whereby quasiparticles in a two-dimensional electron gas acquire fractional charge. The effect appears only in ultrapure samples of graphene.
At the Aspen meeting, the rage was the “quantum twisting microscope,” a new technique developed by the team of Shahal Ilani, a condensed-matter experimentalist at the Weizmann Institute of Science in Israel. Detailed in a February Nature paper, the quantum twisting microscope combines the measuring capability of scanning tunneling microscopes with the manipulation of atomic force microscopy. That combination allows users, for the first time, to adjust the angle of a graphene stack after fabrication. “In terms of technique, it is probably the most spectacular development of the past couple of years,” says Jarillo-Herrero.
Also at the meeting, Ilani announced improvements to the microscope that would allow it to overcome previous complications when operating at small angles and cryogenic temperatures. The technique’s tantalizing potential of continuously observing changes at the magic angle in situ with 0.001° resolution has researchers like Jarillo-Herrero, in his own words, “hyper-excited.”
If magic-angle graphene were of interest only to carbon connoisseurs and superconductivity specialists, it would have been an extraordinary advance. But it has also drawn the attention of a much broader community working with 2D materials. Researchers stacking transition metal dichalcogenides such as tungsten diselenide have taken inspiration from magic-angle graphene to study samples at small twist angles. An analog approach has also made its way to photonics, where twists in silicon crystals have been used to slow light.
Unlike other areas of condensed-matter research on superconductivity, magic-angle graphene has remained relatively scandal-free despite the excitement surrounding it. Jarillo-Herrero attributes this to the openness in graphene research, starting with the Geim and Novoselov group. “I went to Manchester in 2005 to visit and learn how to exfoliate graphene,” he says. “And I think that permeated through the community.”
Theory and experiment have also shared an unusually close bond in tackling the mysteries of magic-angle graphene, Kaxiras says. “It’s very exciting, both from the side of the possible applications and from the challenge to the theory to predict interesting behavior,” he says. “It’s just the perfect type of system to work on.”