A motif of Japanese basket-weaving called the kagome pattern has kept physicists engrossed for years. Kagome baskets are usually created using strips of bamboo woven into an extremely symmetrical pattern of interlaced, corner-sharing triangles.
An illustration depicting a kagome metal — an electrically conducting crystal, made from layers of iron and tin atoms, with each atomic layer arranged in the repeating pattern of a kagome lattice. (Image credit: Felice Frankel; Illustration overlays by Chelsea Turner)
If a metal or other conductive material could be engineered to look like such a kagome pattern at the atomic scale, with each atom arranged in similar triangular patterns, it should, in theory, display rare electronic properties.
MIT, Harvard University, and Lawrence Berkeley National Laboratory have reported in Nature that they have for the first time developed a kagome metal — an electrically conducting crystal, made from layers of tin and iron atoms, with each atomic layer organized in the repeating pattern of a kagome lattice.
When current was conveyed across the kagome layers within the crystal, the researchers saw that the triangular arrangement of atoms induced bizarre, quantum-like behaviors in the passing current. Rather than flowing straight through the lattice, electrons instead swerved or bent back within the lattice.
This behavior is a 3D cousin of the supposed Quantum Hall effect, wherein electrons flowing through a 2D material will display a “chiral, topological state,” wherein they bend into tight, circular paths and flow along edges without any energy being lost.
“By constructing the kagome network of iron, which is inherently magnetic, this exotic behavior persists to room temperature and higher,” says Joseph Checkelsky, assistant professor of physics at MIT. “ The charges in the crystal feel not only the magnetic fields from these atoms but also a purely quantum-mechanical magnetic force from the lattice. This could lead to perfect conduction, akin to superconductivity, in future generations of materials.”
To examine these findings, the team measured the energy spectrum within the crystal, using an advanced version of an effect first exposed by Heinrich Hertz and elucidated by Einstein, known as the photoelectric effect.
“Fundamentally, the electrons are first ejected from the material’s surface and are then detected as a function of takeoff angle and kinetic energy,” says Riccardo Comin, an assistant professor of physics at MIT. “ The resulting images are a very direct snapshot of the electronic levels occupied by electrons, and in this case, they revealed the creation of nearly massless ‘Dirac’ particles, an electrically charged version of photons, the quanta of light.”
The spectra exposed that electrons flow via the crystal in a way that indicates the originally massless electrons gained a relativistic mass, akin to particles called massive Dirac fermions. Theoretically, this is illuminated by the presence of the lattice’s constituent iron and tin atoms. The former are magnetic and produce a “handedness,” or chirality. The latter possess a heavier nuclear charge, creating a large local electric field. When an external current flows by, it senses the tin’s field not as an electric field but as a magnetic one and veers away.
The research team was guided by Checkelsky and Comin, as well as graduate students Linda Ye and Min Gu Kang in partnership with Liang Fu, the Biedenharn Associate Professor of Physics, and postdoc Junwei Liu. The team also includes Christina Wicker ’17, research scientist Takehito Suzuki of MIT, Felix von Cube and David Bell of Harvard, and Chris Jozwiak, Aaron Bostwick, and Eli Rotenberg of Lawrence Berkeley National Laboratory.
“No Alchemy Required”
Physicists have theorized for years that electronic materials could assist exotic Quantum Hall behavior with their intrinsic magnetic character and lattice geometry. It wasn’t until several years ago that scientists made progress in appreciating such materials.
“The community realized, why not make the system out of something magnetic, and then the system’s inherent magnetism could perhaps drive this behavior,” says Checkelsky, who at the time was working as a researcher at the University of Tokyo.
This removed the need for laboratory-produced fields, normally 1 million times as strong as the Earth’s magnetic field, required to observe this behavior.
“Several research groups were able to induce a Quantum Hall effect this way, but still at ultracold temperatures a few degrees above absolute zero — the result of shoehorning magnetism into a material where it did not naturally occur,” Checkelsky says.
At MIT, Checkelsky has instead sought ways to drive this behavior with “intrinsic magnetism.” An important insight, motivated by the doctoral work of Evelyn Tang Ph.D. ’15 and Professor Xiao-Gang Wen, was to pursue this behavior in the kagome lattice. To achieve that, first author Ye ground together tin and iron, then heated the resulting powder in a furnace, creating crystals at about 750 °C — the temperature at which tin and iron atoms favor to arrange in a kagome-like pattern. She then immersed the crystals in an ice bath to enable the lattice patterns to stay stable at room temperature.
“The kagome pattern has big empty spaces that might be easy to weave by hand, but are often unstable in crystalline solids which prefer the best packing of atoms,” Ye says. “ The trick here was to fill these voids with a second type of atom in a structure that was at least stable at high temperatures. Realizing these quantum materials doesn’t need alchemy, but instead materials science and patience.”
Bending and Skipping Toward Zero-Energy Loss
After the researchers managed to grow several samples of crystals, each about a millimeter wide, they gave the samples to colleagues at Harvard, who imaged the individual atomic layers within each crystal using transmission electron microscopy. The resulting images exposed that the arrangement of tin and iron atoms within each layer looked like the triangular patterns of the kagome lattice. Mostly, iron atoms were located at the corners of each triangle, while a single tin atom was located within the larger hexagonal space formed between the interlacing triangles.
Ye then passed an electric current through the crystalline layers and observed their flow via electrical voltages they created. She learned that the charges deflected in a manner that appeared 2D, regardless of the 3D nature of the crystals. The conclusive proof came from the photoelectron experiments conducted by co-first author Kang who, along with the LBNL team, was able to demonstrate that the electronic spectra corresponded to effectively 2D electrons.
As we looked closely at the electronic bands, we noticed something unusual,” Kang adds. “ The electrons in this magnetic material behaved as massive Dirac particles, something that had been predicted long ago but never been seen before in these systems.”
The unique ability of this material to intertwine magnetism and topology suggests that they may well engender other emergent phenomena,” Comin says. “ Our next goal is to detect and manipulate the edge states which are the very consequence of the topological nature of these newly discovered quantum electronic phases.”
Going forward, the team will be exploring ways to stabilize other more highly 2D kagome lattice structures. Such materials, if they can be synthesized, could be used to examine not only devices with zero energy loss, such as dissipationless power lines but also applications covering quantum computing.
“For new directions in quantum information science there is a growing interest in novel quantum circuits with pathways that are dissipationless and chiral,” Checkelsky says. “ These kagome metals offer a new materials design pathway to realizing such new platforms for quantum circuitry.”
This study was supported partly by the Gordon and Betty Moore Foundation and the National Science Foundation.