When Electrons Stop Acting Like Electrons

There is a law of physics that has held remarkably well for 170 years. In 1853, German physicists Gustav Wiedemann and Rudolph Franz noticed something elegant about metals: no matter which metal you picked — copper, silver, gold, iron — the ratio of how well it conducts heat to how well it conducts electricity was always roughly the same at a given temperature. The better a metal is at moving electrons, the better it is at moving heat. The two properties march in lockstep, governed by a constant that carries the names of Lorenz, Wiedemann, and Franz.

This makes deep physical sense. In an ordinary metal, electrons do both jobs simultaneously. The same particles that carry electrical current also carry thermal energy. They are inseparable. Heat and electricity are two faces of the same coin.

Now, a team at the Indian Institute of Science (IISc) in Bangalore has watched that coin shatter.

In a paper published in Nature Physics, researchers led by PhD student Aniket Majumdar and professors Arindam Ghosh and Subroto Mukerjee have observed electrons in graphene entering a state where electrical and thermal conduction are not just different — they move in opposite directions. As one rises, the other falls. The Wiedemann-Franz law is violated by a factor of more than 200 times at low temperatures. Not broken by a small margin. Obliterated.

And the reason why is one of the most beautiful stories in modern physics.

A Single Layer of Carbon That Changes Everything

Graphene needs little introduction: it is a sheet of carbon exactly one atom thick, arranged in the familiar hexagonal honeycomb pattern. Since its isolation by Andre Geim and Konstantin Novoselov won the 2010 Nobel Prize, physicists have discovered that this material is bizarre in almost every way. Electrons in graphene don’t obey the same equations as electrons in copper. They behave instead like massless particles — zipping around at a fixed velocity as if obeying Einstein’s theory of special relativity rather than ordinary quantum mechanics.

But there is a special condition in graphene that has fascinated theorists for years, and which no experiment had fully captured — until now.

The Dirac Point: A Knife’s Edge Between Metal and Insulator

Like many materials, graphene’s electronic behavior depends on how many electrons are present. Add electrons, and it acts like a conductor. Remove them (creating “holes” — the positively-charged absences of electrons), and it acts like one too. But there is an exact midpoint — a precise balance between electrons and holes — called the Dirac point, where the material sits on the knife’s edge between metallic and insulating behavior.

At this point, something extraordinary happens. Individual electrons lose their identity. Rather than moving as separate particles, they interact so strongly with each other that they form a collective fluid — not unlike water molecules flowing together rather than rattling around independently.

This state has a name: the Dirac fluid. And it has been theorized to behave like something that normally only exists in the most extreme environments in the universe: a quark-gluon plasma.

A Liquid That Shouldn’t Exist in a Lab

Quark-gluon plasma is the primordial soup that existed roughly 20 microseconds after the Big Bang, when the universe was so hot and dense that even protons and neutrons couldn’t hold together — their constituent quarks and gluons dissolved into a nearly perfect, nearly frictionless liquid. Today, physicists recreate fleeting glimpses of this state by smashing heavy atomic nuclei together at CERN.

The Dirac fluid in graphene is theorized to be the same kind of thing, but accessible on a laboratory bench. Both share the property of being minimally viscous quantum fluids — they flow with almost no internal resistance, described by the same equations from relativistic hydrodynamics.

But actually measuring this fluid — actually proving that graphene electrons were behaving this way — had proved remarkably stubborn. The Dirac point requires exquisite precision to reach: even a single stray charged impurity in the material can knock electrons off the knife’s edge. Real graphene, made in most labs, is too dirty.

The Key: Impossibly Clean Graphene

The breakthrough in this experiment came from materials. Majumdar and colleagues used hexagonal boron nitride (hBN) as a substrate and protective encapsulation layer for their graphene devices. Hexagonal boron nitride has a crystal structure almost identical to graphene’s honeycomb lattice — but it is electrically inert, acting as a perfectly flat, atomically smooth surface that barely disturbs the graphene above it. Critically, the hBN crystals used in this work were grown by Kenji Watanabe and Takashi Taniguchi at the National Institute for Materials Science in Tsukuba, Japan — some of the purest boron nitride ever produced, a coveted material that has enabled a generation of quantum experiments worldwide.

Sandwiched between two such layers, the graphene device became ultraclean. Electron mobilities — a measure of how freely electrons move without being scattered — reached exceptional levels. The Dirac point was no longer a smeared-out mess; it became a sharp, precise feature that the researchers could tune to with extraordinary accuracy using a simple gate voltage.

Measuring the Unmeasurable

To expose the Dirac fluid, the team did something deceptively simple in concept but fiendishly difficult in practice: they measured both electrical and thermal conductivity of the same graphene device simultaneously, at the same carrier density, at temperatures down to a few Kelvin.

This required building a tiny on-chip thermometer — a resistive element that could detect temperature differences across the graphene, converted to heat flow. They then swept the gate voltage, tuning the carrier density from electron-rich to hole-rich, passing through the Dirac point at the exact center.

In a normal metal, or even in typical graphene, both conductivities would peak at roughly the same carrier density. The Wiedemann-Franz law says they go together.

What they actually measured was the opposite. At the Dirac point, electrical conductivity reached its minimum — as expected at a charge-neutral point. But thermal conductivity reached its maximum. The two had completely decoupled.

“It is amazing that there is so much to do on just a single layer of graphene even after 20 years of discovery,” said Professor Arindam Ghosh, one of the corresponding authors.

What the Numbers Mean

The deviation from the Wiedemann-Franz law is expressed through the Lorenz number — the ratio of thermal to electrical conductivity, divided by temperature. In ordinary metals, this number is a universal constant: L₀ = 2.44 × 10⁻⁸ W·Ω·K⁻². It barely changes between copper and platinum.

At graphene’s Dirac point, the team measured an effective Lorenz number more than 200 times larger than this value. This is not a small discrepancy. It means that heat and electricity have been completely divorced from each other, flowing through fundamentally different mechanisms.

What’s carrying the heat is not the electrons themselves, but the collective oscillations of the fluid — entropy and enthalpy density waves that propagate through the electron liquid. The charge carriers and heat carriers have separated into distinct collective modes, exactly as relativistic hydrodynamics predicts for a fluid near a quantum critical point.

A Universal Constant Emerges

Here is where the story gets even more beautiful. Despite the chaos — despite the Wiedemann-Franz law being dramatically broken — the behavior is not random at all. It is universal.

The team found that both conductivities, though moving in opposite directions, converge on a single underlying constant: the quantum critical conductivity σ_Q. Across multiple different graphene devices, all fabricated and measured independently, σ_Q converged to approximately (4 ± 1) × e²/h — where e is the electron charge and h is Planck’s constant.

This number is quantized. It depends only on fundamental constants of nature and the “universality class” of the quantum critical point — a deep mathematical classification that groups wildly different physical systems into the same family based on the symmetry of their underlying equations. The graphene Dirac point belongs to the same universality class as certain models in high-energy physics. The specific value (4 ± 1) × e²/h was predicted theoretically but had never been measured experimentally. Now it has been, with remarkable consistency across devices.

Approaching the Perfect Fluid Limit

There’s a third result in this paper that connects graphene to something even more unexpected: black holes.

In 2005, physicists used string theory — specifically a mathematical technique called holography or AdS/CFT correspondence — to derive a fundamental lower bound on how viscous any quantum fluid can possibly be. The ratio of a fluid’s dynamic viscosity to its entropy density, they showed, can never fall below ℏ/(4πk_B), where ℏ is the reduced Planck constant and k_B is Boltzmann’s constant.

The quark-gluon plasma created at CERN comes tantalisingly close to this bound — it is the most perfect fluid ever directly observed, less viscous than any classical liquid. The bound is sometimes called the “KSS bound,” named after the physicists who derived it (Kovtun, Son, and Starinets).

Majumdar and colleagues found that in their cleanest graphene devices at near-room temperature, the effective viscosity-to-entropy-density ratio of the Dirac fluid approaches this holographic lower bound within a factor of four.

This makes graphene one of the closest laboratory realizations of a perfect quantum fluid — rivaling the quark-gluon plasma, but accessible with a gate electrode and a dilution refrigerator rather than a multi-billion-dollar particle accelerator.

Why This Matters: Physics at a Crossroads

The practical implications are exciting too. A material whose thermal and electrical conductivities can be tuned independently — and which displays universal quantized transport — is a profound tool for quantum sensing. Devices based on the Dirac fluid could, in principle, amplify extraordinarily weak electrical signals or detect faint magnetic fields with exquisite sensitivity.

But the deeper significance is conceptual. We are living in an era where condensed matter physics — the study of materials — keeps discovering that its equations are secretly the same as those governing cosmology, black holes, and particle physics. Graphene, a material you could peel off a pencil with sticky tape, is reproducing the physics of the first microseconds of the universe and the theoretical properties of black hole horizons.

This shouldn’t be possible. And yet the numbers match, to within a factor of four.

“Since this water-like behaviour is found near the Dirac point, it is called a Dirac fluid — an exotic state of matter which mimics the quark-gluon plasma, a soup of highly energetic subatomic particles observed in particle accelerators at CERN,” explained Aniket Majumdar, the paper’s first author and a PhD student who has just, with this single paper, put his name on a result physicists will be discussing for years.

Twenty Years Is Not Long Enough

Graphene was first isolated in 2004. For the past two decades, an enormous global effort has been poured into understanding it. Thousands of papers. Multiple Nobel Prizes’ worth of discoveries. And yet, as Professor Ghosh observed, there is still so much to do.

The existence of the Dirac fluid has been theorized since almost the beginning of graphene science. The violation of the Wiedemann-Franz law near the Dirac point was predicted. The quantization of σ_Q was calculated. But prediction and measurement are different things — and the gap between them represents all the messy reality of actually building a device, making it clean enough, cold enough, precise enough to see the universe’s secrets hiding inside a single atomic layer.

That gap closed in Bangalore, with a measurement that took years of painstaking work and the collaboration of materials scientists in Japan who grew the perfect boron nitride crystals that made it possible.

A 170-year-old law violated by 200 times. A quantum fluid approaching the holographic perfection limit. A universal constant measured for the first time in any material. All inside one atom of carbon.

Physics is strange and wonderful, and we are nowhere near done.

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The paper, “Universality in quantum critical flow of charge and heat in ultraclean graphene,” was published in Nature Physics, Vol. 21, pp. 1374–1379 (2025), by Aniket Majumdar, Nisarg Chadha, Pritam Pal, Akash Gugnani, Bhaskar Ghawri, Kenji Watanabe, Takashi Taniguchi, Subroto Mukerjee, and Arindam Ghosh. DOI: 10.1038/s41567-025-02972-z. A preprint is available at arXiv:2501.03193.