On the quantum dance floor, the 'twist' is king
In 1986, two relatively unknown physicists, working in a laboratory on a Swiss hilltop, made a discovery that started a revolution.
“It was the Woodstock of condensed matter physics,” said Enrico Rossi, associate professor of physics at William & Mary. “People were so excited. It changed everything.”
Physicists J. Georg Bednorz and K. Alex Mueller discovered superconductivity in ceramic material, specifically lanthanum-based cuprate perovskite, and created the first high-temperature superconductor.
The discovery earned them the 1987 Nobel Prize in Physics and held the promise that one day it could be feasible to transmit electricity and information over vast distances with virtually no loss of current or data.
“They were basically playing with this ceramic material and found that it became a superconductor at temperatures well above absolute zero, well above the limit that theory predicted was possible,” Rossi said.
The typical flow of electric current, the kind that powers the average household, is a charge carried by electrons that move through a circuit made from copper wiring. The electrons move from one atom to another as they travel through the wiring, which creates a current that provides power to the home.
With copper, and almost any other material, there is a certain level of resistance against the moving electrons, sort of like air resistance pushes back on a thrown tennis ball. The less resistance, the better the electrons can move and the current will flow more freely. Superconductivity is a phenomenon in which the resistance against an electric current flowing through a material is zero.
The problem with superconductivity is that it happens at very low temperatures, close to 0 Kelvin or -459.67 degrees Fahrenheit. The idea of room-temperature superconductivity is something like the El Dorado of materials science, Rossi explained.
Such a discovery would pave the way for ultrafast computers, far more efficient power transmission and high-speed trains that could travel hundreds of miles per hour with little power. For now, the City of Gold remains elusive. Bednorz and Mueller earned their Nobel for reaching superconductivity at 35 Kelvin, or -396.67 degrees Fahrenheit.
“There was the hope that we could go all the way up to room temperature,” Rossi said. “That would be a true revolution, because you could have no dissipation in everyday connections. But we’re stuck in lower temperatures and, from an academic perspective, we still don’t understand why these ceramic materials are superconducting.”
Rossi says part of the difficulty may be that ceramic materials have a complicated chemical structure that makes it challenging to identify the key ingredients that lead electrons to superconduct. He and Xiang Hu, a postdoc research assistant in the university’s Department of Physics, are co-authors on a paper recently published in Physical Review Letters, the American Physical Society’s flagship publication.
The duo collaborated with researchers from Microsoft Quantum and the Polish Academy of Sciences to examine what leads electrons to superconduct in twisted bilayer graphene. Their work was supported by an NSF-CAREER grant, the Office of Naval Research, the Army Research Office and the United States-Israel Binational Science Foundation.
Twisted bilayer graphene is a material made from taking a one-atom-thick layer of carbon atoms and folding it over on itself at a slight angle, 1.05 degrees. By folding it at that precise angle (what physicists call the “magic angle”), the atoms line up in such a way that the material becomes a superconductor.
The fundamental mechanism that leads to superconductivity might be the same as in the ceramic materials, but the chemical structure of twisted bilayer graphene is much simpler, Rossi explained. The revelation started a new field called "twistronics" and opened the door for researchers like Rossi and Hu to study the underlying physics of superconductivity.
“It’s really about the way the system is engineered,” Rossi said. “Take, for example, something like chalk. You can break a brick of chalk really easily, but that same material makes shells, which can last for centuries. It has to do with the nature of how the atoms are arranged. That same principle applies for creating superconductivity in graphene.”
Rossi and the team of researchers found that the specific arrangement of atoms, and the way such arrangement affects the quantum state of each electron, can explain why electrons in graphene superconduct.
It helps to think of the phenomenon as a kind of quantum square-dance, with the folded matrix on which the atoms are arranged as the dance floor. The dancers are electrons, who, as the evening goes on, couple up with other electrons in groupings called Cooper pairs, a key element of superconductivity.
“In twisted bilayer graphene, the electrons are forced to move slowly. If you slow them down, make the velocity very small, and you allow the electrons to spend more time in the same place, they start interacting and pairing up,” Rossi said. “Naively, you would also expect that to lead to pure superconductivity, because the electrons have enough time to form pairs and form a lot of them. However, if these Cooper pairs are all by themselves, doing their own thing, then the system is not going to superconduct and conventional results suggest that this would be the case in twisted bilayer graphene.”
In simpler terms, to achieve superconductivity, the quantum square-dance must become a giant conga line with all the Cooper pairs joining together. If couples keep to themselves, the material doesn’t superconduct. Rossi, Hu and their collaborators discovered how this happens in twisted bilayer graphene, despite the extremely small velocity of the electrons.
“The way I like to explain it is that somehow they all need to link arms,” Rossi said. “Imagine there is a chain of people and they’re all going forward, but then they hit an obstacle. If the pairs aren’t linked together, then one pair will stop when they hit the obstacle and the other may keep going.”
If only half the pairs are getting around the obstacle, Rossi explained, then the amount of current the system can carry is cut in half, causing electrical resistance. Half of the pairs are getting stuck. If all the electrons are able to link together, then they can pull each other past obstacles and the electrical resistance shrinks to zero.
“The strength of this linkage is really important,” Hu said. “Using previous results, one would conclude that such strength would be vanishingly small in twisted bilayer graphene. The fact that it's possible for the linkage to be present in twisted bilayer graphene has not been examined before now.”
Once the researchers realized that the “conga line” formation in twisted bilayer graphene was crucial for superconductivity, they set out to figure out why it happens. Instead of looking at the dancers, the team looked at how they dance.
They found it was actually the individual nature of each couple (the electron pairs’ individual attributes, analogous to spin) that had the greatest impact on linkage. It had a greater impact than their size or speed or how much time they spent on the quantum dance floor.
“At first, the focus was on the velocity. When it goes to zero, you can form couples and that’s great, but it’s not enough,” Rossi said. “You need to be able to make all those couples somehow link up. That’s what you need to get superconductivity. The assumption was that this linking was also due to the velocity, but that was neglecting the fact that there is another way. It has to do with the individual features of the quantum states. It’s a contribution people hadn’t considered before.”