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Physics A magic trick: take 2 sheets of coal and spin

In the universe of office supplies, pencil lead – a mixture of graphite and clay that does not contain lead – seems to be unique except for its ability to draw dark lines.

But 15 years ago, scientists discovered that a single graphite sheet – a layer of carbon atoms one atom thick arranged in a honeycomb – is a miracle. This ultra-thin carbon, called graphene, is flexible and lighter than paper, but 200 times stronger than steel. It is also a good conductor of heat and electricity.

Scientists imagined all the unusual things graphene could be made of: transistors, sensors, new materials. But after studying and cataloging its properties, scientists went on to other problems. Practical applications are very slow, because part of what makes graphene attractive – its strength – also makes it difficult to cut the material into precise shapes.

Last year, graphene reappeared on the physics research scene when physicists from the Massachusetts Institute of Technology discovered that stacking two sheets of material, twisted at a slight angle between them, opened a treasure chest with strange phenomena. She started a new field: twistronics.

What happens if two pieces of graphene are stacked on top of each other? If the layers were perfectly aligned, the two layers of graphene would behave essentially the same as a single graphene sheet. But when one of the layers was slightly twisted compared to the other, the rotational misalignment of the two networks causes repeated "moire pattern"Extending to many atoms.

"I just started there," said Dr. MacDonald. "What if they were almost even?"

Electrons can easily jump between two sheets in which their grids were lined up. But in places where they were positioned incorrectly, the flow would be more difficult. In 2011, Dr. MacDonald and Rafi Bistritzer, PhD scientist, he calculated that from a small angle the electronic structure would become "flat" and the electrons would block like cars trying to get through Times Square.

Slowly moving electrons will interact more – "strongly correlated" in the language of physics – and from experience physicists knew that strongly correlated systems are often surprising.

"We threw out a few guesses," said Dr. MacDonald.

The article was intriguing, but largely ignored. Equations, covering many particles at once, are generally too complex to be solved exactly. So Dr. MacDonald and Dr. Bistritzer introduced some simplifications to get rough answers. Many scientists believed that their results were an artifact of their approximations, not a likely description of what could actually be observed.

Philip Kim, a Harvard physicist who conducted many early experiments with graphene – both Dr. Efetow and Dr. Jarillo-Herrero worked in their laboratory – believed that glazed details in calculations were important. "I was skeptical," he said.

But Dr. Jarillo-Herrero decided to test the forecast. "There was good theoretical motivation to see what would happen," he said.

Layers are only loosely bonded and sometimes scientists have noticed that they are returning to perfect alignment. Other times the sheet begins to rotate but stops before it is completely aligned, sometimes it ends up with the desired 1.1 degree. The angle does not have to be exact; behavior appears to occur when the steering angle is between 1.0 and 1.2 degrees.

Last year, Dr. Jarillo-Herrero and his colleagues reported a surprising discovery. Two layers of graphene, now known as magically twisted bilayer graphene, became a superconductor after cooling to a fraction of a degree above absolute zero. (Dr. MacDonald and Dr. Bistritzer did not foresee this.)

"When we saw superconductivity, all hell broke loose," said Dr. Jarillo-Herrero. "Then we realized it was a very important matter."

Despite all the amazing tricks of the original work with graphene, scientists have never been able to transform it into a superconductor. It was a revelation that his behavior can be changed by simply placing another sheet on top and slightly twisting it. It was as if the color of two sheets of paper suddenly changed if one was rotated.

Other experimental physicists have returned to the study of graphene. "I was totally wrong," admitted Dr. Kim. "Allan MacDonald's theory was correct."

In a new Nature article, Dr. Efetov and his colleagues confirmed Dr. Jarillo-Herrero's findings, but found additional permutations of temperature, magnetic field and electron density, which also turn graphene into a superconductor.

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