In a quiet corner of low-temperature physics, researchers have stumbled on a phase of matter that seems to break one of the field’s unwritten rules: it works without well-defined particles. Instead of electrons behaving like tiny billiard balls, they dissolve into collective waves, yet the material still obeys precise mathematical laws. The discovery forces a rethink of how matter can organize itself, and why some of the strangest quantum effects are also the most robust.
At the heart of this story is a new topological state, an emergent pattern in which the usual picture of electrons as individual objects simply fails. The finding builds on years of work on quantum criticality, exotic “in-between” phases, and even supersolid light, but it goes a step further by showing that a material can gain structure precisely because particle-like states are absent. For technology and for basic science, that is a startling twist.
When electrons stop being particles
In conventional metals and semiconductors, I am used to thinking of electrons as quasiparticles, each with a clear energy and velocity that can be tracked through the crystal. The newly reported state of matter overturns that intuition: in this regime, electrons no longer act like individual particles at all, yet the system still displays sharply defined topological behavior. Experiments on a material called CeRu4Sn6 show that at extremely low temperatures it reaches quantum criticality, a knife-edge point where it hovers between competing phases and its electrons behave as extended waves rather than a fog of particles.
What makes this so striking is that the material still exhibits topological order, a kind of global pattern that usually relies on stable quasiparticles. In the new work, researchers describe an emergent state in which there are many topologically unique varieties, even though the usual particle picture has broken down. As Silke Bühler-Paschen, identified in the reporting as Paschen, notes, topological properties can even arise because particle-like states are absent, not in spite of that absence. A separate study on a platform called Until and its companion entity Topologic reinforces this point, showing that electrons can stop acting like particles while the underlying topological rules of physics still hold.
The razor’s edge of quantum criticality
To understand how such an “impossible” phase can exist, I have to look at quantum critical points, special locations in a material’s phase diagram where a continuous transition occurs at absolute zero. At these points, fluctuations never die away, and the system is dominated by collective quantum behavior rather than classical thermal motion. A quantum critical point is defined as the position in the phase diagram where a continuous phase transition takes place at zero temperature, tuned not by heat but by pressure, magnetic field, or chemical doping, as explained in detailed work on quantum critical behavior.
CeRu4Sn6 sits precisely on such a razor’s edge. At the lowest temperatures, it does not settle into a simple ordered phase, but instead hovers in a regime where its electrons are neither localized nor free in the usual sense. In this “in-between” state, the material’s properties are governed by entangled waves that extend across the crystal, giving rise to a new quantum state that earlier theory had considered impossible. The fact that this state is also topological, with robust features that survive imperfections, links quantum criticality directly to the broader family of topological materials prized for their unusual electronic behavior.
Topology without particles
Topological phases are usually introduced with simple analogies, such as the difference between a doughnut and a coffee mug, which share a single hole and can be smoothly deformed into each other. In quantum materials, topology shows up in properties that are insensitive to local disorder, like edge currents that keep flowing even when the surface is rough. Traditionally, these effects are described in terms of electrons moving in special bands, forming protected surface states that behave like massless particles. Yet the new state in CeRu4Sn6 suggests that topology can survive, and even be strengthened, when those particle-like states dissolve.
This is not an isolated hint. An international team has created artificial structures that allow researchers to tune topological properties in a highly controlled way, effectively engineering artificial topological matter whose behavior can be dialed between different regimes. In parallel, experiments on topological insulators have confirmed that when these materials are hit with circularly polarized laser light, their surfaces respond with a unique signature that comes only from the topological surface states. Together with Paschen’s observation that topological properties can arise because particle-like states are absent, these results point to a deeper principle: topology is a pattern in the collective quantum wavefunction, not a property that depends on electrons behaving like neat little bullets.
Hall effects and the geometry of quantum motion
One of the clearest windows into this geometry-first view of matter comes from Hall effects, where electric currents deflect sideways in a magnetic field. In materials that display the anomalous Hall effect, theorists such as Isobe and Nagaosa have shown that electrons with spin pointing up and spin pointing down experience different effective forces, leading to a built-in sideways current even without an external magnetic field. This behavior is tied to the Berry curvature in momentum space, a geometric property of the electronic bands that is inherently topological. The discovery of the quantum anomalous Hall effect, often abbreviated as QAH, provided a striking example of how such geometry can produce quantized edge currents without any external field at all.
The same geometric thinking underpins the spin Hall effect, where spin currents flow sideways even when the net charge current does not. Pioneering work by Mikhail Dyakonov and combined ideas from the anomalous Hall effect, sometimes simply called Hall, with spin-dependent Mott scattering of electrons off nuclei to predict this effect. In both anomalous and spin Hall regimes, what matters is not individual electrons as particles, but the topology of their allowed states in momentum space. The new CeRu4Sn6 phase fits naturally into this picture: it is another case where geometry and topology of the quantum state dictate behavior even when the notion of a single electron trajectory has lost its meaning.
Between solid and liquid, and even in light
The idea that matter can occupy strange middle grounds is not limited to heavy-electron compounds. In atomic systems, Scientists have created a predicted intermediate state between solid and liquid by manipulating light, producing an odd solid that can flow like a liquid. This phase blurs the line between crystalline order and fluid motion, and it is stabilized by carefully tuned optical fields that control how atoms interact. The result is a material that behaves like both a rigid lattice and a flowing medium, a reminder that the familiar categories of solid, liquid, and gas are only rough guides in the quantum world.
Even more dramatically, Italian researchers have managed to transform light itself into a supersolid, a state that combines the rigidity of a crystal with the frictionless flow of a superfluid. In a groundbreaking experiment, these Italian teams engineered photons to organize into a pattern that behaves like both a solid and a fluid at the same time. Separate reporting on Italian scientists emphasizes how this challenges our basic understanding of matter, since light is usually thought of as pure radiation, not something that can crystallize. These hybrid states echo the CeRu4Sn6 discovery: in each case, the system finds a way to occupy two seemingly incompatible roles at once.
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