Quantum physics: new state of matter discovered

Quantum physics tells us that particles behave like waves that therefore their position is space is unknown. Yet in many situations, it still works remarkably well to think of particles in a classical way—as tiny objects that move from place to place with a certain velocity. When physicists describe how electric current flows through metals, for example, they imagine electrons racing through the material and being accelerated or deflected by electromagnetic fields.

Even more modern approaches are based on this particle picture—such as the concept of topological states, whose discovery was honored with the Nobel Prize in Physics in 2016. However, there are materials in which the particle picture completely breaks down (see publication below). In such cases, it no longer makes sense to think of electrons as small particles with a well-defined position or a unique velocity.

Now, a research team at TU Wien has shown that such materials can nevertheless exhibit topological properties—even though these have so far been explained using particle-like behavior. This demonstrates that topological states are more general than previously thought: two seemingly contradictory concepts turn out to be compatible.

When the Particle Picture No Longer Makes Sense

“The classical picture of electrons as small particles that suffer collisions as they flow through a material as an electric current is surprisingly robust,” says Prof. Silke Bühler-Paschen from the Institute of Solid State Physics at TU Wien. “With certain refinements, it works even in complex materials where electrons interact strongly with one another.”

However, there are also situations in which this picture appears to break down completely and the charge carriers lose their particle-like character. This seems to happen in the material composed of cerium, ruthenium and tin (CeRu₄Sn₆), which has now been investigated at TU Wien at extremely low temperatures. “Near absolute zero, it exhibits a specific type of quantum-critical behavior,” says Diana Kirschbaum, first author of the current publication. “The material fluctuates between two different states, as if it cannot decide which one it wants to adopt. In this fluctuating regime, the quasiparticle picture is thought to lose its meaning.”

Topology: Rolls and Donuts

Independently of this discovery, the material was also investigated theoretically, leading to the conclusion that it should host topological states. “The term topology comes from mathematics, where it is used to distinguish certain geometric structures,” explains Silke Bühler-Paschen. “For example, an apple is topologically equivalent to a bread roll, because the roll can be continuously deformed into the shape of an apple. A roll is topologically different from a donut, however, because the donut has a hole that cannot be created by continuous deformation.”

In a similar way, states of matter can be described: the velocities and energies of particles—and even the orientation of their spin relative to their direction of motion—can follow specific geometric rules. This is particularly exciting because it makes topological properties very robust. Small disturbances, such as defects in the material, do not change these properties—just as small deformations cannot turn a donut into an apple. This is why topological effects are of great interest for storing quantum information, in novel types of sensors, and in steering electric currents without magnetic fields.

As abstract and unfamiliar as it may seem to describe the behavior of particles using topology, such descriptions have traditionally still relied indirectly on the classical particle picture. “These theories assume that one is describing something with well-defined velocities and energies,” explains Diana Kirschbaum. “But such well-defined velocities and energies do not seem to exist in our material, because it exhibits a form of quantum-critical behavior that is considered to be incompatible with a particle picture. Nevertheless, simple theoretical approaches that ignore these non-particle-like properties had previously predicted that the material should show topological characteristics.”

Curiosity Pays Off

This presented a clear contradiction. For this reason, Bühler-Paschen’s team initially hesitated to take the theoretical prediction of topology seriously and investigate it further. Eventually, however, curiosity prevailed, and Diana Kirschbaum began searching for experimental evidence of topological states.

Indeed, at extremely low temperatures—less than one degree above absolute zero—she observed behavior that clearly indicates the presence of topological states: a spontaneous (anomalous) Hall effect. In the Hall effect, charge carriers are normally deflected by a magnetic field. However, this deflection can also arise from topological effects, even in the absence of any external magnetic field. What is particularly remarkable is that the charge carriers behave as if they were particles, even though the particle picture seems to fail in this material. “This was the key insight that allowed us to demonstrate beyond doubt that the prevailing view must be revised,” says Silke Bühler-Paschen.

“And there is more,” adds Diana Kirschbaum. “The topological effect is strongest precisely where the material exhibits the largest fluctuations. When these fluctuations are suppressed by pressure or magnetic fields, the topological properties disappear.”

Topological States are More General than Previously Thought

“This was a huge surprise,” says Silke Bühler-Paschen. “It shows that topological states should be defined in generalized terms.” The team refers to the newly discovered state as an emergent topological semimetal and collaborated with Rice University in Texas, where Lei Chen (co–first author of the publication), working in the group of Prof. Qimiao Si, developed a new theoretical model capable of combining the phenomena of quantum criticality and topology.

“In fact, it turns out that a particle picture is not required to generate topological properties,” says Bühler-Paschen. “The concept can indeed be generalized—the topological distinctions then emerge in a more abstract, mathematical way. And more than that: our experiments suggest that topological properties can even arise because particle-like states are absent.”

The discovery has important practical implications, as it points to a new strategy for identifying topological materials. “We now know that it is worthwhile—perhaps even particularly worthwhile—to search for topological properties in quantum-critical materials,” Bühler-Paschen says. “Because quantum-critical behavior occurs in many classes of materials and can be reliably identified, this connection may allow many new ‘emergent’ topological materials to be discovered.”