Quantum Oscillations in an Insulator: A 'Shouldn't Exist' Quantum Phenomenon

Imagine walking into a perfectly soundproofed room — double walls, acoustic foam, an airtight door, all designed so no sound can penetrate. You close the door and expect total silence.

But you hear singing.

Not leaking through the door, not through the walls — but from the room itself, from the floor, the ceiling, the interior of every inch of the "soundproofing material."

In October 2025, University of Michigan physicist Lu Li and his international team experienced the physics version of this moment. They discovered quantum oscillations inside a material that should be "completely insulating" — a phenomenon that for decades was thought to belong exclusively to metals. More shocking still: these oscillations come not from the material's surface, but from deep within its bulk.

The research was published in *Physical Review Letters* and described by peers as "really bizarre and exciting."

The Electrons' Spring Dance

To understand how absurd this finding is, we first need to discuss what quantum oscillations are.

In a metal, electrons are free. They move around like pedestrians wandering a city, unbound. Apply a magnetic field to a metal, and these free electrons orbit around the field lines — like swinging a ball on a string. Physicists call this "cyclotron motion."

If you slowly increase the magnetic field, the electrons' orbits shrink, and each time they shrink to a certain size, they "resonate" with the material's quantum energy levels. It's like pushing a swing: when your pushing frequency matches the swing's natural frequency, it swings highest. In experimental data, this resonance appears as periodic oscillations in physical quantities like resistivity and magnetic susceptibility — the "quantum oscillations."

Li likes a more intuitive analogy: electrons behave like springs. Change the magnetic field, and the spring's vibration frequency changes. Recording these frequencies lets you read out information about the electron world inside the material.

Quantum oscillations are a powerful tool for studying the electronic structure of metals. Since the discovery of the de Haas–van Alphen effect in 1930, physicists have used this method to "listen" to the electronic song inside metals, inferring key properties like the shape of the Fermi surface and effective electron mass.

The key prerequisite: you need free electrons.

Insulators: The Electron Prison

Insulators are a completely different world.

In an insulator, electrons are locked tightly into atomic orbitals — like a city under total curfew, everyone locked at home, no one on the streets. No free electrons, no cyclotron motion, no quantum oscillations. This is basic condensed-matter physics, written into every textbook.

But starting in the 2010s, this common wisdom began to waver.

Scientists observed quantum oscillation signals in several special insulators. Like hearing singing in a soundproof room — it shouldn't be there, but it is.

One explanation quickly became popular: perhaps it's a surface effect. A class of materials called "topological insulators" has insulating bulk but an ultra-thin conductive layer at the surface — like a safe with a solid steel body plated with gold. If the quantum oscillations came only from that surface "gold," everything made sense.

This explanation preserved the textbook while retaining application prospects — the surface conductivity of topological insulators is exactly what quantum computing and novel electronic devices dream of. Everyone breathed a sigh of relief.

But Li's team said: No — the song isn't coming from the surface; it's coming from inside the room.

35 Tesla: Searching for Truth in Extremes

Determining whether the oscillations originate from the surface or the bulk requires extremely strong magnetic fields.

Ordinary lab magnets produce about 10–15 tesla (a hospital MRI is about 1 tesla). Not enough. Li's team went to the National High Magnetic Field Laboratory (National MagLab), home to the strongest artificial magnetic fields in the world.

They placed YbB₁₂ — ytterbium boride, a "Kondo insulator" — into the magnet and ramped the field up to 35 tesla.

What does 35 tesla mean? Roughly 35 times an MRI magnet — enough to levitate a frog (in 2000, Andre Geim levitated a frog at 16 tesla; he later won the Nobel Prize for isolating graphene).

Under these extreme conditions, the team measured YbB₁₂'s heat capacity — the material's ability to absorb heat. Quantum oscillations leave periodic "fingerprints" in heat capacity. If the oscillations came from the surface, the signal would be extremely weak (surface atoms are a tiny fraction); if from the bulk, the signal would be much stronger.

The result was clear: an oscillation frequency of 700 tesla, with a signal strength fully consistent with a bulk origin.

"For years, scientists have been asking a fundamental question: where do the carriers in this exotic insulator come from? Bulk or surface? Intrinsic or extrinsic?" said researcher Chen Guan-Wen (Kenwen Chen). "We're excited to provide clear evidence — it's bulk, and it's intrinsic."

Kondo Insulators: A Self-Contradictory Existence

YbB₁₂ is no ordinary insulator. It's a "Kondo insulator," named after Japanese physicist Jun Kondo.

The story of Kondo insulators is bizarre in itself. At high temperatures these materials actually conduct, but as temperature drops, resistance rises and they become insulators. Counterintuitive — normally, lower temperatures mean better metal conductivity.

The cause is an exotic quantum effect: at low temperatures, the material's "itinerant electrons" and "localized electrons" become strongly quantum-entangled, like two strangers tied together, neither able to move. This entanglement "locks up" the originally free electrons, turning the metal into an insulator.

In YbB₁₂, ytterbium atoms provide localized f-electrons, and the boron framework provides itinerant electrons. At low temperatures, both "perish together," losing their freedom.

But the quantum oscillations tell us: under extreme magnetic fields, these "locked-up" electrons seem to come alive again. The entire material behaves like a metal, even though it's an insulator.

A New Duality: Conductor and Insulator at Once

Li places the discovery in a bigger framework he calls a "new duality."

A century ago, physicists discovered the "old duality": light is both wave and particle; the electron is both particle and wave. This wave-particle duality overturned classical physics, gave birth to quantum mechanics, and ultimately produced lasers, semiconductors, MRI — nearly every modern technology we depend on.

Li believes we may be witnessing the birth of another duality: materials can be conductors and insulators at the same time.

"We have actually demonstrated that the naive picture — good conductivity at the surface, useful for electronic devices — is completely wrong," Li said. "It's the whole compound that behaves like a metal, despite being an insulator."

There's a catch: this "crazy metallicity" appears only under extreme magnetic fields of 35 tesla. In everyday life, YbB₁₂ remains a well-behaved insulator.

"I wish I knew what to do with it, but at this point we have no clue," Li admits. "What we have now is experimental evidence of an extraordinary phenomenon. We've documented it and hope that someday we can figure out how to use it."

The Unknown Carriers

Perhaps the most fascinating part: we still don't know what is oscillating.

In metals, the carriers of quantum oscillations are free electrons — that's clear. But in YbB₁₂, the electrons are locked up by the Kondo effect; there shouldn't be free carriers. So what is undergoing cyclotron motion?

"Confirming the oscillations are bulk and intrinsic is exciting," said graduate student Yuan Zhu, "but we still don't know which kind of neutral particle is responsible for this observation. We hope our findings will stimulate more experimental and theoretical work."

"Neutral particle" — the phrasing is careful, and intriguing. If the carriers were charged, they would presumably be some kind of electron; but if they're neutral, they might be an entirely new quasiparticle, something we don't yet understand.

Throughout physics history, every "signal that shouldn't exist" ultimately pointed to new physics. In 1964, Gell-Mann predicted quarks; in 1974, Ting and Richter discovered the J/ψ particle; in 2012, the Higgs boson was finally captured. Each time, there was first a "signal that shouldn't be there," then a new understanding of the world.

Could the quantum oscillations in YbB₁₂ be the next such signal?

Curiosity Before Applications

Li is honest: he doesn't know what this discovery is good for.

In an era that demands research be "useful," such honesty is nearly a luxury. But the history of science tells us that the deepest breakthroughs often come from "useless," curiosity-driven research.

When quantum mechanics was born, no one knew what it could be used for. The Schrödinger equation, Heisenberg's uncertainty principle — these seemed like purely intellectual games. But decades later, they became transistors, lasers, MRI, smartphones — the foundations of modern civilization.

The Kondo effect is the same. When Jun Kondo proposed his theory in 1964, it was only to explain a tiny low-temperature anomaly in metal resistance — a "useless" little problem. But the Kondo effect later became a cornerstone for understanding heavy-fermion materials, high-temperature superconductivity, and quantum critical phenomena.

Perhaps the quantum oscillations in YbB₁₂ will follow the same path. Today it's just a "really bizarre" phenomenon, a puzzle that makes physicists scratch their heads. But maybe in fifty years, someone will invent technology we can't imagine today based on this "signal that shouldn't exist."

Or maybe not. But that's the charm of basic science — you never know where curiosity will take humanity, but you must first let it set out.

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*References:*

• *Quantum Oscillations in the Heat Capacity of Kondo Insulator YbB₁₂, Physical Review Letters (2025), DOI: 10.1103/ms3x-pjsk*
• *University of Michigan News: "Really bizarre and exciting: The quantum oscillations are coming from inside"*
• *ScienceDaily: "Really bizarre quantum discovery defies the rules of physics"*