September 28, 2026 -- Copper is typically an excellent electrical conductor, but when cooled to low temperatures, magnetic impurities can disrupt the flow of electrons and cause its electrical resistance to increase. Known as the Kondo effect, the physics of this phenomenon has been understood for decades, but predicting its behavior accurately in specific materials has remained challenging. Now researchers are probing how the same effect reshapes the motion of electrons in quantum materials.

For the first time, researchers from Yale University and Caltech used computational strategies to accurately predict material-specific Kondo behavior in real metals. Unlike previous methods, which use simplified models, the team’s first-principles approach used the actual material’s atomic and electronic structures to describe this quantum problem.

Their findings, published in the journal Science(Link is external) (Link opens in new window), represent a step toward developing high-accuracy quantum chemistry methods for simulating complex quantum materials, such as high-temperature superconductors and quantum magnets.

The lead authors of the paper are Professor Tianyu Zhu of Yale Chemistry and Dr. Linqing Peng of Princeton University, who both started this study while working in the lab of Professor Garnet Chan at Caltech.

We demonstrated this method can simulate a challenging quantum materials problem with better accuracy than state-of-the-art approaches,” said Zhu. “That is really exciting because of where we could further lead this research direction—to simulate more diverse, more important materials science problems.”

The Kondo conundrum

The Kondo effect, which is actually a physics puzzle, is fairly straightforward. Normally, as a metal—like copper—cools down, its atoms vibrate less, allowing electrons to flow more freely to conduct electricity. However, a strange thing can happen when copper is cooled to a very low temperature. The conductivity becomes worse.

This occurs when there are impurities in the copper, maybe a little bit of iron or nickel in it, which have their own electrons. Those electrons behave very differently than the copper electrons. As this bulk material cools below the Kondo temperature, the impurity’s magnetic moment becomes screened by the surrounding conduction electrons, and scattering increases, causing the metal’s electrical resistance to rise.

Over the last few decades, computational physicists and material scientists have been testing methods to try to quantitatively describe this universal phenomenon that’s present in many quantum materials,” said Zhu. “The problem is whether we can use computational methods to correctly describe this phenomenon and understand what’s going on at the atomic level, or electron level.”

Historically, scientists have simplified the problem into a much smaller model by reducing the material’s electronic structure. Although it’s easier to calculate, a lot of key information is lost in the process.

A different approach

Using a first-principles approach—starting from the material’s atomic and electronic structure rather than reducing it to a simple low-energy model—the team performed calculations on this Kondo problem. They used several computational strategies they developed over the years centered around a quantum embedding framework to directly tackle the real material itself.

Specifically, they took quantum chemistry technology originally designed to describe molecules and applied it to a copper material setting.

This is not even a chemistry problem. This is a physics problem,” said Zhu. “But many of the computational techniques we developed and applied to solve this problem are adapted from high-accuracy quantum chemistry.”

Those techniques allowed the team to treat the magnetic impurities almost like molecules while retaining a detailed many-body description of their interactions.

In the study, they simulated a series of seven different transition-metal atoms (impurities) embedded in copper. Their numerical results successfully reproduced key trends in experimental measurements for this series of Kondo systems, with greater accuracy than standard model-based calculations. In the process, they also found new physical insights as to why specific Kondo properties are different from one impurity to the next.

This pioneering simulation technique represents a step toward understanding the grand challenges of quantum materials. With that door open, the Zhu Group is already pushing the research in new directions.

New Kondo research on the leading edge

The Zhu Group is currently working on two projects related to these Kondo effect findings.

The first project involves advanced magnetic materials used in applications such as memory and computing devices. In collaboration with Professor Yu He’s group in Yale Engineering’s Department of Applied Physics, Zhu is studying two-dimensional magnetic materials that host a variety of competing magnetic phases, with potential relevance to memory and computing technologies.

In another study, Zhu is applying related many-body computational methods to understand single-atom alloy catalysis. In heterogeneous catalysis, scientists often rely on a metal surface to catalyze small molecule transformations. In this case, isolated atoms of one metal are embedded in the surface of another, creating impurity sites that can boost the catalytic efficiency. The computational strategies used in the original study are transferable to this one.

“The work on the Kondo effect presents very exciting opportunities for future research on important materials science problems,” said Zhu.

Study co-authors are Huanchen Zhai, Zhi-Hao Cui, and Runze Chi, along with senior and co-corresponding author Garnet Kin-Lic Chan of Caltech. The research was funded by the Air Force Office of Scientific Research, the US Department of Energy, Office of Science, Basic Energy Sciences, and the US National Science Foundation.