Precise disorder

Sometimes disorder has its upsides. Sometimes everything doesn’t have to stack up neatly. Sometimes it is the little deviations from the norm that help us discover new things and inspire groundbreaking ideas.

Physicist Dmitri Efetov is a master of this controlled disorder. Born in Bochum and with research posts in Barcelona, at the Massachusetts Institute of Technology and Columbia University, Efetov has held the Chair of Experimental Solid State Physics at LMU since August 2021, but he doesn't stack books or printed studies. Efetov stacks graphene, a special, ultra-thin form of carbon. And by stacking it in a deliberately disorderly manner, he creates effects that one day could be very helpful in quantum computing or in rendering possible the lossless transmission of electricity. Above all, however, Efetov’s stacking leads to a new, still largely obscure domain of physics: twistronics.

Such surprises are par for the course with graphene. It has always been seen as an everyday kind of wonder material. It is found in pencils, for example. When the graphite tip glides over the surface of a sheet of paper, individual layers of carbon are left behind: graphene. The material is just one atomic layer thick and has a hexagonal structure like honeycomb or incredibly fine chicken wire.

Although this geometric structure had long been known, it was not until 2004 that physicists managed to produce and measure an individual layer of the material – with amazing results: Graphene is lighter than paper yet 200 times stronger than steel. It is a good heat conductor, and it conducts electricity better than most metals. The electrons in the graphene are responsible for these properties. They behave like light particles zipping through the world without mass and at almost the speed of light.

As if two leaves suddenly changed color

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When the Nobel Prize in Physics 2010 was awarded for the discovery of graphene, people thought we had a wonder material on our hands. It promised to revolutionize the world – from superconducting transistors to strong, lightweight tennis rackets. But the revolution did not happen and the material disappointed in practical applications. Graphene fell out of fashion, including in research. “We had the feeling back then that we knew almost everything there was to know about this material, and that no more major surprises were to be expected,” says Dmitri Efetov. “As a basic researcher, that’s not likely to get the juices flowing.”

But then the field got a fresh twist. Researchers asked themselves: What happens if we stack layers of graphene – but not as neatly as in the graphite of a pencil, where one atom sits on top of another, rather in a somewhat untidier fashion?

A team from Massachusetts Institute of Technology (MIT) in the United States was the first to acquire the knack. In a paper published in the journal Nature in March 2018, the group led by Pablo Jarillo-Herrero was able to demonstrate that two graphene layers, when twisted relative to each other by 1.1 degrees, exhibit surprising properties. Depending on the temperature, magnetic field, and applied potential, the physicists were able to transform the material into an isolator or else a superconductor in which electrons no longer experience any resistance. It was as if two leaves suddenly changed color as soon as they were given a little twist. A new physics was born: twistronics, a portmanteau of “twist” and “electronics.”

Efetov, then still at the Institute of Photonic Sciences in Barcelona, joined the party in 2019. Together with his team, he managed to demonstrate the effect, becoming only the third research group worldwide to accomplish this feat. And that was not all: The team also managed to capture the external conditions at which the stack becomes superconducting in greater detail.

Slowed down like traffic during rush hour

What goes on in this stacked graphene is still not fully understood. What is clear is that the hexagonal structures of the two skewed graphene layers interfere with each other. If you print the pattern on to two sheets and twist them relative to each other, darker and brighter patches are revealed through the unequal superposition of the respective lines. A much larger pattern, also hexagonal in shape, becomes apparent.

The Moiré effect is the name of this phenomenon, which also affects the electrons in the graphene, as the new, superimposed structure changes their distribution. Formerly moving at lightspeed, they are now slowed down like traffic in rush hour. This has consequences: Suddenly the electrons feel the effects of each other, they interact, they become “strongly correlated” as they say in physics.

Precisely this correlation is a major topic in modern solid-state physics – theoretically still largely not understood, with many open questions and hopefully many surprises. “Single layers of graphene never offered us such interacting electrons,” says Efetov by video link.

Research with correlated electrons overlaps in places with another insufficiently understood field of physics: superconductivity at relatively high temperatures. The whole enterprise is about much more than theoretical games. Should scientists one day succeed in transporting electricity at room temperature without loss, it would revolutionize energy supply. Answers to the questions as to why and under what conditions electrons in twisted graphene no longer experience any resistance could yield decisive clues.

Initial findings from Efetov’s laboratory indicate, moreover, that twistronics affords insights into magnetic phenomena, in isolators and even in exotic states which have been associated with the physics of black holes. “Before now, these issues have arisen only in various materials,” says Efetov. “For them all to exist in one material – in twisted graphene – is new and opens up a huge playground and a previously unknown area of physics.”

Just graphite and ordinary adhesive tape

Furthermore, the material is comparatively simple to manufacture. Transparent adhesive tape from an office drawer is sufficient, as it was for the discovery that led to the Nobel Prize. Efetov sticks a strip of tape to a graphite crystal and pulls it off again. Layers of graphene remain adhered to the tape. Using a plastic stamp, he lifts up one of these layers, twists it by 1.1 degrees, and lays it upon the other. Done. “Just in terms of the concept, it’s easy-peasy,” says Dmitri Efetov. “You can really picture it like two sheets of paper that are overlaid at a slight angle.”

When it comes to specifics, things are of course not quite so simple. The twisted layers like to move back, as it were, into the neatly stacked original position of the graphite. They tense up when they are rolled over each other. They do not rest flat. Anyone who has ever tried to roll a protective film over the screen of a smartphone and was driven to despair by the air bubbles underneath the film will have some insight into the problem. “It took years and years until we found a method that delivered good results,” says Efetov.

1.1 degrees: the magic angle

In a cleanroom much like the one currently being modified to facilitate research into graphene layers at LMU, Efetov fixes tiny contacts to a carbon sandwich. Then he puts the sandwich into a sort of super refrigerator called a cryostat. As superconductivity only occurs from minus 272 degrees Celsius, the sample has to be cooled almost to absolute zero. Once all that is done, the measurements can finally begin.

The scientific interest centers upon how the electrons move in the double-layered graphene. To this end, Efetov and his team apply a little voltage to the contacts. Given that we are talking about just a few billionths of a volt, however, the word “small” is actually a big exaggeration. The team varies this voltage and checks how this affects the current flowing through the sample. On the scale of a few trillionths of an ampere, the current is measured. It is amplified, the noise is suppressed, and then – hopefully – it reveals what is going on in the graphene.

But Efetov’s maltreatment of the material is not limited to electrical voltage. He also uses laser light – and here, too, the material exhibits strange behavior. So strange in fact that it furnishes one of the possible applications of twisted graphene: If a particle of light falls on the structure, the latter falls back from its superconducting state into its normal state, which the measuring devices immediately register. “With such a detector, we can measure the dimensions of an individual light particle,” says Efetov. This is of interest for quantum computers, for example, which are currently being developed and use light for their calculations. But such a device could also be used in quantum communication, where information is conducted through fiber optic cables such that it cannot be intercepted and then has to be detected.

Opening the door to a new physics

This is still in the realm of theory, and there is much left to discover in twistronics. Research teams have just begun to stack more than two twisted layers. They have now investigated three, four, and even five graphene layers – always in the hope of being able to push superconductivity into higher temperature ranges, and ultimately in the direction of room temperature. As of yet, this does not look like succeeding. But it remains an open question as to whether this is impossible in principle or is merely foundering due to poorly stacked graphene. Furthermore, other materials such as molybdenum sulfide, a lubricant that is also made up of individual layers and can therefore be stacked, present an interesting avenue for research.

Efetov is pursuing a different approach: Some of today’s high-temperature superconductors are also layered. Why not extract a layer, stack it skewed over a second layer, and see what happens? Maybe the temperature will rise.

More than any application, however, it is the fundamental physics, the new world of twisted layers that most interests Dmitri Efetov. With stacked graphene, a comparatively easy method now exists for diving into this world to discover its peculiar rules and derive physical insights. Disorder is thus a means to an end: “We want to understand these exotic states,” says Dmitri Efetov. “The stacking of materials is the tool that opens the door to this physics.”

Alexander Stirn

Prof. Dmitri Efetov has held the Chair of Experimental Solid State Physics at LMU since 2021. Born in 1980, Efetov studied physics at ETH Zurich and carried out research for his diploma thesis at Columbia University in New York, where he subsequently did his Ph.D. After that, he switched as a postdoctoral researcher to Massachusetts Institute of Technology (MIT), before moving in 2017 to the Institute of Photonic Sciences (ICFO) in Barcelona. In 2019, the European Research Council awarded him a prestigious Starting Grant.

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