MIT Physicists Trap Electrons in a 3D Crystal for the First Time

The results open the door to investigating superconductivity and other exotic electronic states in three-dimensional materials.

Electrons move through conductive material like commuters during Manhattan rush hour. The charged particles may bump and collide with each other, but for the most part they don’t concern themselves with other electrons as they hurtle forward, each with their own energy.

But when the electrons of a material are captured together, they can end up in exactly the same energy state and behave as one. This collective, zombie-like state is known in physics as an electronic “flat band,” and scientists predict that when electrons are in this state, they can begin to sense the quantum effects of other electrons and act in coordinated, quantum ways. Then exotic behavior such as superconductivity and unique forms of magnetism can arise.

Discovery of the 3D flat tire

Now, physicists of OF have successfully captured electrons in a pure crystal. It is the first time that scientists have realized an electronic flat band in a three-dimensional material. With some chemical manipulation, the researchers also showed that they could transform the crystal into a superconductor – a material that conducts electricity without resistance.

The rare electronic state is due to a special cubic arrangement of atoms (pictured) that resembles the Japanese art of ‘kagome’. Credit: Courtesy of the researchers

The trapped state of the electrons is possible due to the atomic geometry of the crystal. The crystal that the physicists synthesized has an arrangement of atoms that resembles the woven patterns in ‘kagome’, the Japanese art of basket weaving. In this particular geometry, the researchers found that instead of jumping between atoms, electrons became ‘trapped’ and settled into the same energy band.

Potential applications and research motivation

The researchers say this flat band state can be achieved with virtually any combination of atoms – as long as they are arranged in this kagome-inspired 3D geometry. The results, published on November 8 in the journal Natureoffer scientists a new way to investigate rare electronic states in three-dimensional materials. These materials could one day be optimized to enable ultra-efficient power lines, supercomputing quantum bits, and faster, smarter electronic devices.

“Now that we know we can make a flat tire from this geometry, we have great motivation to study other structures that may have other new physics that could be a platform for new technologies,” said study author Joseph Checkelsky, associate professor of physics. .

Checkelsky’s MIT co-authors include graduate students Joshua Wakefield, Mingu Kang and Paul Neves, and postdoc Dongjin Oh, who are co-lead authors; graduate students Tej Lamichhane and Alan Chen; postdocs Shiang Fang and Frank Zhao; undergraduate Ryan Tigue; associate professor of nuclear science and engineering Mingda Li; and associate professor of physics Riccardo Comin, who collaborated with Checkelsky to lead the research; together with employees from several other laboratories and institutions.

Setting up a 3D trap

In recent years, physicists have successfully captured electrons and confirmed their electronic flat-band state in two-dimensional materials. But scientists have found that electrons trapped in two dimensions can easily escape from the third, making flat band states difficult to maintain in 2D.

In their new research, Checkelsky, Comin and their colleagues sought to realize flat bands in 3D materials so that electrons would be confined in all three dimensions and any exotic electronic states could be maintained more stably. They had the idea that kagome patterns might play a role.

In previous work, the scientists observed trapped electrons in a two-dimensional lattice of atoms that resembled some kagome designs. When the atoms were arranged in a pattern of interconnected triangles that shared the corners, the electrons remained confined to the hexagonal space between the triangles, instead of jumping across the lattice. But like others, the researchers discovered that the electrons could escape up and out of the lattice through the third dimension.

The team wondered: Could a 3D configuration of similar lattices work to trap the electrons? They searched databases of material structures for an answer and came across a particular geometric configuration of atoms, commonly classified as pyrochlore – a type of mineral with a highly symmetrical atomic geometry. The pychlor’s 3D structure of atoms formed a repeating pattern of cubes, with the surface of each cube resembling a kagome-like lattice. They found that this geometry could, in theory, effectively trap electrons in each cube.

Rocky landings

To test this hypothesis, the researchers synthesized a pyrochlore crystal in the laboratory.

“It’s not much different from the way nature makes crystals,” Checkelsky explains. “We put certain elements together – in this case calcium and nickel – and let them melt at very high temperatures, cool them, and the atoms on their own will arrange themselves into this crystalline, kagome-like configuration.”

They then looked to measure the energy of individual electrons in the crystal, to see if they did indeed fall into the same flat energy band. To do this, researchers typically conduct photoemission experiments, during which they shine a single light photon of light on a sample, which in turn emits a single electron. A detector can then accurately measure the energy of that individual electron.

Scientists have used photoemission to confirm the flat band condition in various 2D materials. Due to their physically flat, two-dimensional nature, these materials are relatively easy to measure with standard laser light. But for 3D materials the task is more challenging.

“For this experiment you generally need a very flat surface,” Comin explains. “But if you look at the surface of these 3D materials, they look like the Rocky Mountains, with a very undulating landscape. Experiments with these materials are very challenging, which is one reason why no one has shown that they harbor trapped electrons.”

The team overcame this hurdle with angle-resolved photoemission spectroscopy (ARPES), an ultra-focused beam of light that can focus on specific locations on an uneven 3D surface and measure the individual electron energies at those locations.

“It’s like landing a helicopter in very small places in this rocky landscape,” says Comin.

Using ARPES, the team measured the energies of thousands of electrons in a synthesized crystal sample in about half an hour. They found that the electrons in the crystal overwhelmingly exhibited the exact same energy, confirming the flat band state of the 3D material.

On the way to superconductivity

To see if they could manipulate the coordinated electrons into an exotic electronic state, the researchers synthesized the same crystal geometry, this time using atoms of rhodium and ruthenium instead of nickel. On paper, the researchers calculated that this chemical exchange should shift the electrons’ flat band to zero energy – a state that automatically leads to superconductivity.

And indeed, they found that when they synthesized a new crystal, with a slightly different combination of elements, in the same kagome-like 3D geometry, the crystal’s electrons showed a flat band, this time in superconducting states.

“This presents a new paradigm for thinking about how to find new and interesting quantum materials,” says Comin. “We showed that with this special ingredient of this atomic arrangement that can hold electrons, we always find these flat bands. It’s not just a stroke of luck. From this point on, the challenge is to optimize to realize the promise of platband materials, which may be able to maintain superconductivity at higher temperatures.”

Reference: “Three-dimensional flat bands in pyrochlore metal CaNi2” by Joshua P. Wakefield, Mingu Kang, Paul M. Neves, Dongjin Oh, Shiang Fang, Ryan McTigue, SY Frank Zhao, Tej N. Lamichhane, Alan Chen, Seongyong Lee, Sudong Park , Jae-Hoon Park, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Anil Rajapitamahuni, Elio Vescovo, Jessica L. McChesney, David Graf, Johanna C. Palmstrom, Takehito Suzuki, Mingda Li, Riccardo Comin and Joseph G. Checkelsky , November 8 2023, Nature.
DOI: 10.1038/s41586-023-06640-1