Researchers at University of California Berkeley, Washington University in St. Louis and Lawrence Berkeley National Laboratory have stacked two sheets of graphene on top of each other and twisted them, which resulted in the conversion of a common linear material into one with nonlinear optical capabilities. This could prove useful for various everyday technologies — from spectroscopy and material analysis to communications and computing.

In the study of optics, scientists distinguish between linear and nonlinear materials. Most materials, including sheets of graphene, are linear. If you shine red light at a sheet of graphene, the photons will either be absorbed or scattered, but in any case - they will remain red.

Nonlinear materials can combine multiple photons into one. The frequency of the resulting photon — which scientists call a “second harmonic generation” — is double that of the original, so it has twice the energy. If you shine red light at a nonlinear material, two red photons combine to create an ultraviolet photon. Scientists use this process to stimulate photo-chemical reactions that need high-energy photons, such as photocatalysis and photosynthesis. More common are the laser pointers that rely on nonlinear crystals to convert invisible infrared photons into green photons.

Nonlinear materials are rare, and their ability to alter photons is usually well-defined and can’t be changed. But in their new study, the team showed that by twisting two layers of graphene in opposite directions, it’s possible to fine-tune their ability to combine photons.

“Just by introducing this twisting mechanism, electrons in the graphene layers have very different behaviors,” said Jie Yao, associate professor of materials science and engineering and the paper’s senior author. “The results are better than we thought. The nonlinear capability generated by twisting graphene layers is surprisingly strong.”

That such a simple action has such a strong effect is due to the fact that a material’s properties are defined at the atomic level.



A graphite crystal is formed of atomically thin sheets of graphene. While the carbon atoms in a sheet of graphene are chemically bonded, the sheets themselves are loosely stacked on top of each other and held together by a relatively weak attractive force, called a Van der Waals force.

Atoms in a sheet of graphene are arranged in a hexagonal honeycomb pattern. A graphite crystal found in nature will be made up of sheets of graphene stacked in one of two highly ordered ways: The atoms in one layer will either sit directly on top of the atoms in another, or they will position themselves above the hexagonal void.

By twisting the sheets of graphene in opposite directions, the symmetry of their atomic arrangement is altered and the atoms’ valence electrons are disturbed. The properties of graphene change.

The weak Van der Waals force holding sheets of graphene together is what makes it possible to separate and twist them. Fuyi Yang, a Ph.D. student in Yao’s lab and the paper’s lead author, used tape to peel layers of graphene off a large graphite crystal. She pressed that graphene sheet onto a substrate of silicon and silicon dioxide and peeled the tape away.

Yang then used a piece of glass outfitted with a small cube of sticky transparent polymer to pick up a piece of hexagonal boron nitride, which can attract sheets of graphene like a magnet. By raising and lowering the nitride with a vertical stage, Yang could lift a second piece of graphene off the silicon substrate and, like a crane loading shipping containers onto a truck, place it onto the first layer at an angle. The whole process takes more than two hours.

In the end, Yang produced 30 samples of bilayer graphene at varying twist angles. With increasing twist angles, the team was able to combine higher energy photons into one.

While the research showed that turning graphene into a nonlinear material is possible, Yao said it’s just a milestone toward the ultimate goal: To make two layers of graphene twist on command.

“That’s one potential direction for future exploration,” Yao said. “If we can change the twisting angle between two graphene sheets in real time, then changing the nonlinear property of that bilayered graphene would be as simple as tuning a radio.”

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