A team of scientists from Caltech and Yale University has shown for the first time how to accurately quantify an important quantum phenomenon in metals, called the Kondo effect, for specific real materials. Unlike previous approaches, which for decades have relied on simplified models to qualitatively describe the effect, the new work uses the actual atomic and electronic structures of materials to solve the problem directly.
The work represents a step toward simulations of important quantum materials such as high-temperature superconductors, in which the motions of individual electrons depend so sensitively on what other electrons are doing at any moment that they cannot be averaged together.
The team describes the new technique and results in a paper published in the July 30 issue of the journal Science . The lead authors of the paper are Linqing Peng (PhD '25) and Tianyu Zhu of Yale University. Both Peng and Zhu started working on the project in the lab of Garnet Chan , Bren Professor of Chemistry and director of the Rudolph A. Marcus Center for Theoretical Chemistry at Caltech.
"It is now possible to predict the properties of some complicated materials purely through computation without referring to experiment," says Chan, who is the senior author of the paper and a Simons Investigator in Physics. "These first materials that we have studied are like a baby step, or a prototype problem, along the way to more complex phenomena such as high-temperature superconductors and quantum magnets."
The Kondo Effect—A Many-Body Problem
For many of the materials used in computing, including semiconductors such as silicon, the interactions between electrons are so weak that they are insignificant in terms of understanding overall behavior. But to learn more about so-called strongly correlated materials needed for quantum applications, pinning down how electrons interact and bounce off each other is crucial.
The Kondo effect comes into play in the simplest example of such a strongly correlated material: the case where a single magnetic atom, such as iron or manganese, is embedded as an impurity in a metal, such as copper. When that bulk material is cooled below a certain temperature (known as the Kondo temperature), something odd happens. When a normal metal is cooled, its electrical resistance decreases steadily, making the material a better conductor at lower and lower temperatures. When a metal with a magnetic impurity reaches its Kondo temperature, its resistance reaches a minimum and then actually increases.
"That is the signature of the Kondo effect, and it's a property of the electrons in the impurity interacting with the electrons traveling through the bulk metal," Chan explains.
Physicists in the 1970s (including, importantly, alumnus Kenneth Wilson, PhD '61) established a theoretical understanding of the general physics around the Kondo effect. It is a prototypical example of what physicists call a many-body problem, because it involves trying to describe the behavior of a system with many, many particles—in this case, electrons in the metal—that interact in complex ways, making it impossible to solve by looking at the behavior of each particle independently. In this case, the magnetic atom has unpaired electrons, and their spin gives the atom its magnetism. At higher temperatures, the vector of that magnetism, the atom's magnetic moment, fluctuates freely. But as the temperature drops, electrons in the metal begin to interact strongly with the atom's spin and can actually flip their own spin to cancel out a bit of the atom's magnetic moment. This extra scattering interaction causes the characteristic leveling off and then increase in resistance associated with the Kondo effect. Eventually, when the whole cloud of electrons gets involved, it masks the atom's magnetism completely.
The electrons in the metal enveloping the atom collectively arrange themselves into a cloud that "screens," or cancels out, the atom's magnetism.
Solving the Problem Quantitatively
The Kondo effect is one of the most intensively studied problems in quantum many-body physics, in part because it is relatively simple to state. It is used as something of a benchmark that researchers must show they can approximate for new theoretical and computational methods to be accepted. But pinning down the precise way in which the resistance decreases and then comes back up or the exact temperature at which the change occurs for a given impurity in a real material has not been possible until now.
Previous methods have simplified the problem by reducing a material's electronic structure to a small number of orbitals—spaces around an atom's nucleus where electrons are most likely to be found—and then applying an approximate mathematical model to that reduced system.
Chan and his team took a different approach. They used technology that had been developed to very accurately describe molecules in the quantum chemistry field and applied it to this material setting. This allowed them to fully describe the magnetic atom impurities as though they were molecules without having to simplify their interactions.
In the paper, the researchers provide results for seven different transition-metal atoms embedded in copper. For most elements, the new method's predictions exceeded the accuracy of model-based calculations by as much as two orders of magnitude.
"We are in an exciting era in which faithful predictive quantum descriptions of the full chemical complexity of real materials are coming within reach," says Peng. "It is becoming realistic to predict material-specific behavior of correlated electrons from first principles, even in some of the most challenging classes of quantum materials.
"This is an important step toward computationally designing materials whose functions emerge from intricate correlated physics, such as high-temperature superconductivity, where the large chemical space and competition among many phases call for predictive theory to help focus the experimental search for new materials," she adds. "I am excited to see what new materials breakthrough this theory will enable in the future."
Additional Caltech authors of the paper, "Toward an exact quantum many-body treatment of Kondo correlation in magnetic impurities" are Huanchen Zhai, a former postdoctoral scholar; Runze Chi, a current postdoctoral scholar; and Zhi-Hao Cui (PhD '23), who completed the work as a graduate student. The work was supported by the Air Force Office of Scientific Research through the Multidisciplinary University Research Initiative program, the US Department of Energy and its Center for Molecular Magnetic Quantum Materials, and the US National Science Foundation.