Coexisting Kondo and Weyl-like transport in kagome heavy-fermion metal, Yb$_y$Co$_3$G$e_{3-x}$Sn$_x$

In the world of solid materials, electrons usually behave like a crowd of people moving through a busy street. Sometimes, they move freely and quickly, like a light breeze. Other times, they get stuck or slowed down by interactions with their neighbors, becoming heavy and sluggish. Scientists have long known how to create materials where electrons act like heavy particles, a phenomenon driven by strong internal forces that effectively weigh them down. They have also discovered materials where electrons behave as if they have no mass at all, zipping through the crystal structure with the speed and lightness of particles in a vacuum. These two behaviors—being heavy and being massless—usually belong to different families of materials. The challenge for physicists has been to find a single substance where both behaviors exist at the same time, allowing them to study how these opposing forces interact within one solid object.

A team of researchers has now found such a material. By growing crystals of a specific compound containing ytterbium, cobalt, germanium, and tin, they discovered a metal where electrons can be both heavy and massless simultaneously. The material, a variation of a kagome metal, acts as a unique laboratory where two distinct types of electron traffic flow side by side without merging into a single, indistinguishable stream. The researchers found that while some electrons become heavy due to magnetic interactions, others remain light and massless, responding to magnetic fields in a way that suggests they are following a different set of physical rules. This discovery offers a new way to control how electricity moves through a material, potentially allowing scientists to switch between heavy and light behaviors without needing to alter the material's chemical composition or apply external tuning.

The story begins with the crystal itself. The researchers grew thin, hexagonal needles of a material called Yb$_y$Co$_3$Ge$_{3-x}$Sn$_x$. Inside these needles, the cobalt atoms form a specific geometric pattern known as a kagome lattice, named after a traditional Japanese woven basket pattern. This arrangement is famous for creating unusual electronic states. Interspersed within this cobalt network are atoms of ytterbium, a rare-earth element. The amount of ytterbium in the crystal was carefully adjusted, with the best samples containing between 19 and 48 percent of the available spots filled. The researchers grew these crystals using a molten tin bath, a method that allowed them to control the disorder and the specific arrangement of atoms with high precision.

When they cooled these crystals down to very low temperatures, the electrons began to show signs of becoming heavy. As the temperature dropped below about 25 Kelvin, the electrical resistance of the material started to rise, a classic sign that the electrons were interacting strongly with the magnetic moments of the ytterbium atoms. This is known as the Kondo effect, where the electrons effectively drag a heavy cloud of magnetic influence with them as they move. As the temperature dropped even further, the resistance peaked and then began to fall sharply. This drop signaled that the heavy electrons had organized themselves into a coherent state, moving in unison across the entire crystal lattice. The researchers measured the heat capacity of the material and found that the electrons were indeed extremely heavy, with a mass enhancement that placed this material firmly in the category of heavy-fermion metals.

However, the story did not end with heavy electrons. When the researchers applied a strong magnetic field along the length of the crystal needle, parallel to the flow of electricity, something unexpected happened. In a typical heavy-fermion metal, the electrical resistance would eventually stop changing as the magnetic field got stronger, reaching a saturation point. But in this material, the resistance kept dropping, becoming more negative as the magnetic field increased, all the way up to a massive 32 Tesla. This behavior did not fit the standard model for heavy electrons. Instead, it matched a signature associated with massless particles called Weyl fermions. In these systems, when an electric field and a magnetic field are aligned, a quantum effect known as the chiral anomaly allows electrons to flow with less resistance, creating a negative magnetoresistance that grows with the square of the magnetic field strength.

To understand how both behaviors could exist in the same crystal, the researchers looked at the electronic structure using a technique called angle-resolved photoemission spectroscopy. This method allowed them to map out the energy levels of the electrons inside the material. They found two distinct types of electronic bands. One set of bands was flat, meaning the electrons in these states did not move easily and were responsible for the heavy-fermion behavior. The other set of bands was dispersive, meaning the electrons could move freely and quickly, behaving like the massless particles associated with topological materials. Theoretical calculations confirmed that the flat bands came from the ytterbium atoms, while the dispersive bands originated from the cobalt kagome network.

The key finding is that these two groups of electrons, though living in the same crystal, largely kept to their own lanes. The heavy electrons, driven by the ytterbium atoms, followed the rules of the Kondo effect, scaling their behavior in a way that matched a single magnetic ion. Meanwhile, the massless electrons, flowing through the cobalt network, responded to the magnetic field with the chiral anomaly. The researchers tested whether the heavy electrons could be the source of the massless behavior, but the data ruled this out. The heavy electrons saturated their response at lower fields, while the massless signal continued to grow. They also ruled out other common explanations, such as disorder in the crystal or simple scattering effects, which could not account for the specific way the resistance changed with the magnetic field.

This separation of behaviors suggests a new picture of how strong correlations and topology can coexist. In some previous theories, the heavy-fermion effect was thought to create the massless states, or to suppress them entirely at low temperatures. Here, the two effects appear to be independent, arising from different parts of the electronic structure. The ytterbium atoms provide the heavy, correlated electrons, while the cobalt lattice provides the topological, massless electrons. Because these two types of electrons are distinct, they can be observed and measured separately within the same bulk material. This means that scientists do not need to tune the material's chemical composition or change its Fermi level to access one behavior or the other; both are naturally present and active.

The implications of this discovery extend beyond just understanding a single material. It demonstrates that it is possible to engineer a solid where different electronic states retain their unique identities even in the presence of strong interactions. This opens the door to selectively accessing correlated and topological responses within a single device. By understanding how these distinct states coexist, researchers may eventually be able to design materials where they can switch between heavy and light conduction modes, or use one type of electron to control the other. The work confirms that the kagome lattice is a fertile ground for such physics, offering a platform where the complex dance of electrons can be untangled into its constituent parts, revealing a world where electrons can be both heavy and light at the same time.