< https://www.quantamagazine.org/graphenes-new-twist-reveals-superconductivitys-secrets-20210316/ >

for the last three years, electrons have been toying with physicists.

the game started in 2018 when the lab of pablo jarillo-herrero announced the find of the decade: when the researchers stacked one flat sheet of carbon atoms on top of another, applied a “magic” 1.1-degree twist between them, then cooled the atomic wafers to nearly absolute zero, the sample became a perfect conduit of electrons.

how were the particles conspiring to slip flawlessly through the graphene sheets? the kaleidoscopic “moiré” pattern created by the skew angle seemed significant, but no one knew for sure. to find out, researchers started twisting and stacking every material they could get their hands on.

at first, the electrons played along. experiment after experiment found that, in an array of flat materials, frigid temperatures brought plummeting electric resistance. a more profound understanding of the conditions necessary for ideal conduction felt close, and with it, a tantalizing step toward an electronics revolution.

“it seemed like superconductivity was everywhere,” said matthew yankowitz, a condensed matter physicist at the university of washington, “no matter what system you looked at.”

but the electrons proved coy. as researchers inspected their samples more carefully, the instances of superconductivity vanished. in some materials, resistance wasn’t actually getting down to zero. in others, different tests offered conflicting results. only in the original double x-x-x-x-layered graphene did electrons regularly achieve a frictionless flow.

“we had this zoo of different twisted materials, and twisted bix-x-x-x-layer graphene was the only one that was clearly a superconductor,” yankowitz said.

then in the past month, two papers published in the journals nature and science described a second related superconductor, a three-x-x-x-layer graphene sandwich with the “bread” sheets aligned and the filling sheet skewed by 1.56 degrees. the unmistakable electron-carrying prowess of twisted trix-x-x-x-layer graphene confirms that the two-wafer system was not a fluke. “it was the first of a family of moiré superconductors,” said jarillo-herrero, a physicist at the massachusetts institute of technology who also led one of the new experiments, “and this one is the second member of the family.”

importantly, this second sibling has helped to illuminate an underlying mechanism that could be what powers the superconductivity of these materials.

in the months after the 2018 discovery, one group of theorists began to puzzle over the mechanism that made bix-x-x-x-layer graphene superconduct. they suspected that one particular geometric trait might allow electrons to swirl into exotic maelstroms that behave in an entirely novel manner. this mechanism, which is unlike any of the (few) known schemes responsible for superconductivity, would explain the superconductive success of bix-x-x-x-layer graphene, as well as the failure of other materials. it also predicted that graphene’s trix-x-x-layer sibling would superconduct as well.

but it remained just a theory — at least until labs had a chance to test it. “from what we know now, it seems like an exciting direction,” said eslam khalaf, a researcher at harvard university who helped develop the model. “it’s not every day that we have a new way to get superconductivity.”

three miracles

in a messy world where friction abounds and particles never really sit still, a phenomenon as perfect as superconductivity has no right to exist. yet everyday x-x-x-x-metals like mercury regularly pull it off at low temperatures, heike kamerlingh onnes discovered by accident in the early 20th century.

the secret was that near absolute zero, vibrations in a x-x-x-x-metal’s atomic lattice steer free electrons into pairs. these couples cooperate in ways individual electrons can’t, forming a unified quantum mechanical “superfluid” that flows through a material without a single electron-atom collision (which would generate heat and resistance). the original theory of superconductivity, developed back in 1957, described it as a delicate electronic dance that all but the most ideal environments would disrupt. “it’s kind of a miracle they pair at all, because the electrons repel each other very strongly,” said ashvin vishwanath, a theoretical physicist at harvard.

researchers caught electrons performing a second miracle in 1986, this time in a family of copper compounds known as cuprates. the materials were somehow able to keep superconducting at dozens of degrees above the temperature that would normally split conventional electron pairs. a new mechanism seemed to be in play, one likely involving mainly electrons themselves, rather than their atomic x-x-x-x-frame.

but after decades of intense study, researchers still aren’t sure exactly how electrons in cuprates orchestrate their superconducting ventures. predicting the behavior of electron collectives involves a brute-force calculation of each particle’s effect on every other particle — a calculation whose complexity increases exponentially with the number of electrons. in order to understand even a tiny fleck of a superconductor, theorists would need to grasp the behavior of electron swarms numbering in the trillions. current simulations can handle about a dozen.

experimentalists aren’t in a much better position. they can grow new crystals, swapping this atom for that, and test their properties. but the materials don’t reveal what the electrons are doing inside. and researchers don’t know how a material will behave until they actually fabricate it. “no one could say i’m going to make this new [cuprate],” yankowitz said, “and predict what the [temperature where it superconducts] is going to be. that’s just a laughably difficult task right now.”

the unique features of twisted bi-x-x-x-x-layer graphene made it more transparent than the cuprates. rather than forging a whole new substance, experimentalists could tweak graphene’s properties with nothing more than an electric field, making it, to many researchers, a “playground” for superconductivity.

“that’s the exciting problem and the wonderful thing about twisted bi-x-x-x-x-layer graphene,” said subir sachdev, a condensed matter physicist at harvard. “it gives a whole new set of tools to investigate how the electrons are moving around.”

it also offered theoretical guidance. at the magic angle of precisely 1.1 degrees, the honeycomb lattices of graphene fuse in such a way that normally zippy electrons slow to a crawl — physicists describe the material as having “flat bands.” sluggish electrons spend more time together, giving them the chance to organize.

but the guidance was vague. electrons in materials with flat bands can socialize in many ways, of which forming superconductive pairings is just one. researchers stacked many atomic wafers at band-flattening magic angles, but the superconductive lightning refused to be bottled.

they seemed to be missing something crucial.

swirling skyrmions

soon after the march 2018 discovery of superconductivity in twisted graphene, vishwanath and his colleagues set about trying to demystify the magic angle and understand what might be holding electrons together.

writing down a theory that fully captured the movement of unruly electrons in bi-x-x-x-x-layer graphene was impossible, so the theorists started by imagining particles that were a bit better behaved. they treated graphene’s hexagonal lattice as two sublattices of triangles. as the electrons move from atom to atom, they usually jump to an atom on the opposing grid. occasionally, a rebel hops to an atom on the same grid.

vishwanath and company insisted that the electrons always switch grids. this choice made splitting the hexagonal grid into triangular grids cleaner mathematically. and in bi-x-x-x-x-layer graphene, with its two x-x-x-x-layers, it brought out an otherwise obscure feature that would eventually become important: the electrons, when constrained in this way, started to move as if they were under the influence of a magnetic field. specifically, electrons on one sublattice appeared to feel a positive magnetic field while electrons on the other sublattice felt a negative one. the theorists didn’t quite recognize it, but the key to a new theory of superconductivity was staring them in the face.

after using the theory to derive the magic angle of 1.1 degrees in bi-x-x-x-x-layer graphene in august of 2018, vishwanath and his colleagues started to pile on more graphene x-x-x-x-layers. the theory, which had originally been designed for two x-x-x-x-layers, snapped onto the new structures far better than expected. they found that they could compute the magic angle for one graphene stack after another with simple ratios that seemed impervious to the increasing complexities of the thicker systems.

“especially in condensed matter physics, you think that you’re doing something very close to physical or even practical reality,” vishwanath said. “but every now and then you get this glimpse of this very ideal world that’s living behind.”

as the group, including collaborators at the university of california, berkeley, explored further, adding more realistic details to the theory, superconductivity appeared, but in an entirely new way. perhaps it wasn’t pairs of electrons that were forming, but tempests of electrons known as skyrmions. since bix-x-x-x-layer graphene has two x-x-x-x-layers, it has four sublattices, but the sublattices with the same magnetic charge act as one. the effective magnetic fields make electrons visiting atoms on one grid want to point up, while electrons on the other grid want to point down. this configuration can lock the electrons into place so that the system behaves as an insulator. (curiously, experiments in cuprates and twisted bix-x-x-x-layer graphene suggest that both materials act like insulators just before they start superconducting).

but if you disturb the balance with additional charge, the electrons on each sublattice can assume a collective vortex pattern — a skyrmion — where the spinning electron at the eye of the storm points up (or down) and its neighbors flatten in a spiral-like pattern.

although thousands of electrons can go into a graphene skyrmion, the vortex acts as if it’s one particle with the charge of one electron. you might expect the negative skyrmions to repel one another, but the quantum mechanical rules governing how electrons hop between the two sublattices actually draw skyrmions on the opposing grids together. in other words, they form pairs of electron-like charges — the fundamental requirement for superconductivity.

key to the skyrmion story is the 180-degree rotational symmetry that dictates electron transfers between the triangular sublattices. a rectangle has that same symmetry. a hexagon has it. a rectangular or hexagonal lattice has it. but stacking and twisting sheets of just about anything besides graphene breaks it. at last, vishwanath and his colleagues were able to explain why the zoo of twisted lattices had failed to superconduct.

“this was the moment where everything fit together,” said khalaf.

theory meets graphene

jarillo-herrero had already been thinking that good things might come in threes. electrons in materials with flat bands move slowly enough for the particles to work together, but superconductivity might get a boost from “dispersive” bands, where the pairs travel more easily. twisted bix-x-x-x-layer graphene has the former. a single x-x-x-x-layer of graphene has the latter. stacking them together might give us the best of both worlds.

then came the prediction from vishwanath’s group that 1.5 degrees was the magic angle for conjuring up superconducting skyrmions in three-x-x-x-x-layers of graphene.

with these arguments in mind, jarillo-herrero’s lab, as well as the lab of philip kim at harvard, set to work making three-x-x-x-x-layer stacks of graphene sheets. both labs saw everything the theorists had predicted and more.

if bix-x-x-x-layer graphene is a playground for superconductivity, trix-x-x-x-layer graphene appears to be the state fair. not only can experimentalists fine-tune the number of electrons in the lattices, they can also shuffle electrons between the x-x-x-x-layers at will with a second electric field. with this flexibility, researchers can seek superconductive sweet spots by making the electrons feel as if they’re moving through a two x-x-x-x-layer system, a one-x-x-x-layer system, or any number of hybrid systems.

using this unprecedented tunability, the labs verified that, unlike other twisted materials, trix-x-x-x-layer graphene passes every test of superconductivity. they also found several indirect hints that superconductivity occurs in an unusual way.

first, the electrons cooperate extremely well. in conventional superconductors, where clusters of atoms pair free electrons, just 1 in 100,000 electrons join the superconducting superfluid. in the cuprates, about 1 in 30 free electrons participate. but in the trix-x-x-x-layer system, researchers estimate that as many as 1 in 10 take part.

the entities in the superconducting pairs — whether they’re electrons or skyrmions — also stay quite close together. the ends of electron duos in supercooled aluminum separate by 10,000 times the general distance between electrons, like a soup of lengthy pasta strands. in trix-x-x-x-layer graphene, however, superconducting couples pack together like macaroni, with the objects sitting just as close to their partner as to their neighbors.

given how hard it is to know what’s happening inside a material at the subatomic level, it’s too early to say whether skyrmions are definitely doing the superconducting in multix-x-x-x-layer graphene. but for khalaf, the strange behaviors seen by jarillo-herrero and kim fit with the electron vortices.

unlike standard electron pairings, skyrmion couples bind tightly for highly efficient superconductivity. the composite objects are also large and crammed close together.

and in standard x-x-x-x-metals, if you put the electrons into a state where they can choose from many possible activities, you usually get the strongest superconductivity. but when researchers gave electrons in the trix-x-x-x-layer system this freedom, superconductivity died. perhaps, said khalaf, it’s because the increased freedom lets the skyrmions fall apart.

“i don’t think it’s definitive that it’s not a conventional superconductor,” said cory dean, a condensed matter physicist at columbia university. but he said that the unusual response to increased freedom “is certainly a data point pointing in the other direction.”

if the rotational symmetry vishwanath and his colleagues identified truly is crucial to multix-x-x-x-layer graphene’s superconductivity, materials scientists could someday use that fact to guide them through a field of many billions of possible substances toward a lattice that can keep its electrons together on a warm day.

the charges in twisted graphene are spread far too thin across the giant moiré cells to superconduct at high temperatures, but the bond holding them together — whether it’s skyrmions or something else — seems strong. further scrutiny of twisted graphene and the theories that explain its odd properties could, researchers hope, distill the essence of its robust superconductivity and point the way toward a lattice that can take more heat.

“if you get the same skyrmion physics on the [atomic] scale,” sachdev said, “then you could really use this.”

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