Scientists working in laboratories at temperatures colder than outer space have stumbled upon a form of matter that according to established theory should not exist. The discovery, published in Nature Physics, threatens to rewrite fundamental assumptions about quantum materials and could accelerate the race toward revolutionary electronics worth hundreds of billions of dollars.
Researchers at TU Wien in Austria, working alongside international colleagues, made the startling find while experimenting with a compound called CeRu4Sn6, a crystalline material formed from cerium, ruthenium, and tin. What they observed left them struggling to reconcile experimental reality with theoretical predictions that had stood for decades.
The material displayed properties characteristic of what physicists call a Weyl-Kondo semimetal, a topological state of matter with extraordinary electronic characteristics. Yet it did so under conditions where such behavior should have been impossible. The electrons within the material had lost their particle-like properties entirely, entering what scientists describe as a quantum critical state where normal rules break down.
Lead researcher Diana Kirschbaum and her team cooled the material to within fractions of a degree above absolute zero, temperatures around negative 272 degrees Celsius. At these extreme conditions, quantum effects dominate and materials can exhibit behaviors impossible at room temperature. What happened next caught everyone off guard.
Below one Kelvin, roughly negative 272 Celsius, the material began generating a spontaneous voltage across its surface without any applied magnetic field. This spontaneous Hall effect serves as a smoking gun signature of topological properties, specifically the presence of Weyl nodes, special points in the electronic structure where quantum states cross.
The finding would be remarkable enough on its own. Topological materials represent one of the hottest areas in condensed matter physics, with potential applications ranging from ultra-low-power transistors to quantum computers. Three researchers won the 2016 Nobel Prize in Physics for their theoretical work predicting these exotic states of matter.
But the Vienna discovery goes further. Standard theory holds that topological states depend on well-defined particle-like excitations called quasiparticles. These quasiparticles form the foundation for how physicists describe electrons moving through solid materials. Remove the quasiparticles, and the topology should vanish with them.
CeRu4Sn6 refused to follow the script.
The material sits naturally at a quantum critical point, a special condition where it teeters on the edge between different quantum phases. At such points, thermal and quantum fluctuations become so strong that quasiparticles cease to exist as meaningful entities. The electrons enter a regime physicists call a non-Fermi liquid, where conventional descriptions fail.
Despite this loss of particle behavior, the topological signatures persisted. The spontaneous Hall conductivity reached values around 100 times larger than theoretical predictions for ordinary topological semimetals, though smaller than the giant response seen in Ce3Bi4Pd3, the first confirmed Weyl-Kondo semimetal.
The research team conducted an extensive series of experiments to map out exactly when and where this strange phase appears. They subjected samples to hydrostatic pressures up to 24,000 times atmospheric pressure while simultaneously varying magnetic field strength and temperature.
The results revealed a dome-shaped region in the material’s phase diagram. At the center of this dome, where pressure and magnetic field equal zero, the quantum criticality reaches maximum strength. The topological signatures peak here as well. As researchers increased either pressure or magnetic field, both effects weakened in tandem.
Specific heat measurements under pressure showed that the quantum critical fluctuations gradually diminish as pressure rises. Analysis of this data allowed the team to extract the Weyl velocity, a parameter describing how fast electrons move through the topological bands. The Weyl velocity increased with pressure, indicating that the electronic correlations weakened as the system moved away from the quantum critical point.
Magnetic field experiments told a similar story. Even tiny fields of just a few millitesla sufficed to suppress the topological response. This extreme sensitivity stands in sharp contrast to Ce3Bi4Pd3, where much larger fields are needed to eliminate the Weyl nodes through Zeeman coupling effects.
The pattern emerging from all measurements points to an inescapable truth. The quantum criticality itself somehow stabilizes the topological state. Rather than competing phenomena, they appear deeply intertwined. The topological phase emerges from the quantum critical fluctuations like a phoenix rising from flames.
This presents a major puzzle for theorists. How can topology survive without quasiparticles? The very definition of band topology relies on Bloch states and Berry curvature, concepts built on the particle picture of electrons.
The research team collaborated with theorists at Rice University to tackle this question. They studied a model heavy-fermion system that captures the competition between different types of magnetic interactions. The model realizes a Kondo destruction quantum critical point, where quasiparticles are eliminated.
Calculations showed that even at this critical point, where thermal energy becomes the only relevant scale, the single-particle spectral functions retain crossing points. These crossings occur at specific locations in momentum space dictated by crystalline symmetry. Remarkably, these crossings display all the hallmarks of Weyl nodes despite the absence of quasiparticles.
The key insight is that symmetry constraints remain robust even when interactions destroy quasiparticles. The eigenfunctions of the electronic Green’s function, a mathematical object describing how electrons propagate through the material, form representations of the space group just like Bloch functions do in non-interacting systems.
Where symmetry forces these eigenfunctions to be degenerate, the corresponding spectral functions must cross. At such crossings, one can define a frequency-dependent Berry curvature that integrates to a quantized Berry flux, the mathematical signature of a topological node.
This formulation extends the concept of topology beyond the standard quasiparticle framework. It provides a rigorous way to identify topological phases in strongly correlated systems where traditional band theory breaks down. The theoretical work validates what the experiments revealed: genuine topology can exist in quantum critical metals.
The discovery opens up a new design principle for finding topological materials. Rather than searching through databases of non-interacting band structures, researchers can now target quantum critical points in correlated materials. Since there are established methods for tuning systems to such critical points through pressure, magnetic field, or chemical substitution, this strategy could prove highly effective.
Scientists have long observed that emergent phases often appear near quantum critical points. The most famous example is unconventional superconductivity, which typically forms a dome around these special points. The highest superconducting transition temperatures occur near the tuning parameter values where quantum critical behavior emerges.
The topological phase discovered in CeRu4Sn6 shows an analogous dome structure. This parallel suggests that a common mechanism may underlie both phenomena. Thermodynamic arguments indicate that entropy accumulates at quantum critical points and gets released as new phases form. For superconductivity, this entropy release binds Cooper pairs and restores Fermi liquid behavior. For the emergent Weyl-Kondo semimetal, the situation differs crucially.
Topological phases are not characterized by order parameters like superconductivity. They have no thermal phase transition and no instantaneous entropy release. The Weyl-Kondo semimetal itself remains a non-Fermi liquid, with quantum critical signatures persisting into the topological phase. This makes the emergent topology fundamentally different from emergent superconductivity.
Future experiments could test whether shot noise, a measure of electron correlations, shows reduced values characteristic of non-Fermi liquids throughout the topological phase. Measurements of entanglement might also reveal whether the emergent semimetal displays enhanced quantum correlations compared to conventional topological materials.
The work demonstrates that CeRu4Sn6 is intrinsically quantum critical without any tuning. Zero-field muon spin rotation measurements confirm the absence of magnetic order down to 50 millikelvin. Inelastic neutron scattering data show scaling collapses indicative of genuine quantum criticality beyond standard order-parameter fluctuations.
This intrinsic quantum criticality places CeRu4Sn6 at a special point in the phase diagram of heavy-fermion materials. These compounds, built from rare earth or actinide elements, exhibit enormous effective electron masses due to strong interactions. They sit between metals and Kondo insulators, which develop a full gap in their electronic structure.
The semimetallic state occupies this intermediate regime. It has larger energy scales than heavy-fermion metals but smaller than Kondo insulators. This makes it ideal for hosting topological nodes while remaining accessible to quantum critical fluctuations.
Density functional theory calculations predicted in 2017 that CeRu4Sn6 should host Weyl nodes near the Fermi energy. The material crystallizes in a non-centrosymmetric structure, lacking inversion symmetry. Combined with strong spin-orbit coupling from the heavy constituent elements, this promotes topological band crossings.
The electrical resistivity shows typical semimetallic behavior, increasing modestly as temperature drops. The Hall coefficient saturates to a small finite value at low temperatures, corresponding to an effective carrier concentration of 0.014 per unit cell. Both observations support the classification as a semimetal rather than a full insulator or simple metal.
What makes the current discovery special is not merely confirming the topological character. Rather, it is demonstrating that this topology emerges from and coexists with quantum criticality in a regime where standard theoretical frameworks predict its impossibility.
The phase diagram constructed from experiments under pressure and magnetic field shows the topological signatures forming a dome centered on the quantum critical point. As control parameters move the system away from criticality, the Weyl-Kondo semimetal weakens and eventually disappears. Maximum topology coincides with maximum correlation strength.
Scientists involved in the research expect this situation may not be unique to CeRu4Sn6. The interplay between quantum criticality, symmetry, and topology could prove to be a general feature of certain material classes. This amounts to a new search strategy for correlation-driven topological phases.
The research teams will continue monitoring developments in related compounds and similar quantum critical systems. With the framework now established for understanding how topology can emerge from quantum criticality, the race is on to find other materials displaying this remarkable behavior. Each new discovery could bring practical quantum technologies closer to reality.
Source:
Kirschbaum, D.M., Chen, L., Zocco, D.A. et al. “Emergent topological semimetal from quantum criticality.” Nature Physics (2026). https://doi.org/10.1038/s41567-025-03135-w
