In a groundbreaking 2025 study, researchers at the Indian Institute of Science (IISc) in Bengaluru have observed electrons in ultra-clean graphene behaving as a nearly perfect quantum fluid, leading to a dramatic violation of the Wiedemann-Franz law, a cornerstone of metal physics established in 1853.
The Wiedemann-Franz law states that in metals, the ratio of electronic thermal conductivity (κ) to electrical conductivity (σ) is proportional to temperature:
L = κ / (σ T) ≈ L₀ = (π²/3) (k_B² / e²)
(where L₀ is the Sommerfeld value, k_B is Boltzmann’s constant, and e is the electron charge). This holds because in Fermi liquids (typical metals), charge and heat are carried by the same quasiparticles, electrons near the Fermi surface.
In ultra-clean graphene near the charge neutrality point (also called the Dirac point), the team found the Lorentz ratio L / L₀ exceeds the expected value by more than 200 times at low temperatures, with electrical and thermal conductivities showing an inverse relationship: as σ increases, κ decreases (and vice versa).
Why Graphene is Special: Relativistic Dirac Fermions
Graphene is a single layer of carbon atoms in a hexagonal honeycomb lattice.
Its low-energy excitations are massless Dirac fermions, described by a linear dispersion relation:
E = ± ħ v_F |k|
(where v_F ≈ 10⁶ m/s is the Fermi velocity, much slower than c but relativistic-like). The band structure touches at Dirac cones (six in the Brillouin zone, effectively two valleys).
At the Dirac point (zero doping, chemical potential μ = 0), graphene is a semimetal: no Fermi surface in the doped sense. Thermal excitations create equal electrons and holes, forming an electron-hole plasma.
In ordinary metals (Fermi liquids), electron-electron scattering is suppressed at low T due to Pauli exclusion. But in graphene near the Dirac point:
- Carrier density n ~ T² (thermal population).
- Scattering rate τ_ee⁻¹ ~ T² (due to linear spectrum and Coulomb interactions).
- This leads to strong interactions and collective behavior.
When electron-electron collisions dominate over impurity or phonon scattering (achieved in ultra-clean, hBN-encapsulated samples), the system enters the hydrodynamic regime: electrons flow collectively like a viscous fluid.
This Dirac fluid is quasi-relativistic, analogous to the quark-gluon plasma in high-energy physics.
Mechanism of the Violation
In hydrodynamics, charge and heat transport decouple:
- Electrical current responds to electric fields but is damped by viscosity.
- Heat current (energy flow without net charge) can flow more freely in neutral plasmas.
Relativistic hydrodynamic theory predicts:
- Electrical conductivity σ approaches a universal, quantized value near the Dirac point (independent of sample details).
- Thermal conductivity κ diverges or becomes very large.
- Result: Inverse correlation between σ and κ, and giant Lorentz ratio enhancement.
The viscosity η is ultra-low approaching the quantum lower bound $η/s ≥ ħ/(4π k_B)$ (where s is entropy density), making it one of the most perfect fluids known.
Earlier hints (e.g., 2016 Science paper) showed ~10x violation, but the 2025 IISc work in Nature Physics reports >200x, confirming quantum-critical universality.
Implications
- Tabletop analog for extreme physics: quark-gluon plasma, black hole thermodynamics (holographic duality/AdS-CFT connections).
- Insights into quantum criticality and entanglement.
- Potential applications: ultra-sensitive quantum sensors, efficient thermoelectric devices (by tuning decoupling).
This discovery, published in Nature Physics (Majumdar et al., 2025), reaffirms graphene’s status as a platform for probing fundamental quantum many-body physics.
Sources:
- Majumdar et al., Nature Physics (2025): “Universality in quantum critical flow of charge and heat in ultraclean graphene”.
- IISc press release & ScienceDaily (2025).
- Related earlier work: Crossno et al., Science (2016).
Physics continues to surprise stay tuned for more from the quantum world!
The Striking Analogy Between Graphene’s Dirac Fluid and Quark-Gluon Plasma
One of the most exciting aspects of the recent discovery in ultra-clean graphene where electrons form a Dirac fluid that dramatically violates the Wiedemann-Franz law is its deep connection to quark-gluon plasma (QGP), the exotic state of matter recreated in heavy-ion collisions at accelerators like RHIC and LHC.
Both systems exhibit nearly perfect fluid behavior with ultra-low viscosity, making graphene a “tabletop” analog for extreme high-energy physics phenomena usually only accessible in cosmic or collider settings.
Key Similarities
- Relativistic (or Quasi-Relativistic) Fermions
- In graphene near the Dirac point, electrons and holes behave as massless Dirac fermions with linear dispersion $(E = \hbar v_F |k|) (v_F ≈ c/300)$.
- In QGP (at temperatures ~10¹² K), quarks and gluons are deconfined and effectively massless due to asymptotic freedom in QCD, also following relativistic dynamics.
- Strongly Interacting, Hydrodynamic Flow
- Both are dominated by particle-particle collisions rather than impurities or lattice scattering.
- When electron-electron (in graphene) or quark-gluon (in QGP) scattering rates are high, the system “hydrodynamizes” quickly: collective flow described by relativistic hydrodynamics emerges on long scales.
- In graphene’s Dirac fluid: Poiseuille (parabolic) flow profiles observed in channels, whirlpools, and negative local resistance.
- In QGP: Elliptic and triangular flow patterns in expanding fireballs match hydrodynamic predictions.
- Ultra-Low Viscosity: Nearly Perfect Fluids
- The hallmark is a low ratio of shear viscosity to entropy density η/s.
- Quantum lower bound from holography (AdS/CFT): $η/s ≥ ħ/(4π k_B) ≈ 0.08 $(in natural units).
- QGP: $η/s ≈ 0.1–0.2 $(one of the lowest known, behaves like a “perfect liquid”).
- Dirac fluid in graphene: $η/s ≈ 0.4–1 × (ħ/(4π k_B))$ at room temperature, remarkably close for a condensed matter system.
- This minimal viscosity enables frictionless-like collective motion despite strong interactions.
- Quantum Criticality and Planckian Dissipation
- Both are near quantum critical points: scattering rates saturate at the Planckian limit τ ≈ ħ/(k_B T), the fastest possible relaxation.
- Decoupling of charge and heat transport in graphene’s Dirac fluid mirrors neutral plasma modes in QGP.
Why This Analogy Matters
- Tabletop High-Energy Physics: Graphene allows controlled experiments (room temperature, tunable gating) on phenomena like relativistic hydrodynamics, once confined to multi-billion-dollar colliders or the early Universe (fraction of a second after Big Bang).
- Insights Across Fields: Helps probe black hole thermodynamics (via AdS/CFT duality), quantum entanglement, and universal bounds on transport.
- Experimental Milestones:
- Graphene: 2016 (Science) ~10x WF violation; 2025 (Nature Physics) >200x, universal conductivity.
- QGP: RHIC/LHC elliptic flow confirms perfect fluidity since ~2005.
This bridge between condensed matter and high-energy physics highlights how a simple carbon sheet can mimic the hottest, densest matter in the cosmos—truly a window into fundamental quantum many-body dynamics!
The Graphene Dirac Fluid and Quark-Gluon Plasma Analogy – With Simple Everyday Examples
The connection between electrons in graphene and the quark-gluon plasma (QGP) – the super-hot soup of fundamental particles from the early Universe or particle colliders – sounds abstract. But it boils down to both behaving like nearly “perfect” fluids that flow with almost no friction, despite constant collisions between particles.
Here are simple analogies to make it clearer:
1. Electrons in Ordinary Metals vs. Graphene’s Dirac Fluid: Traffic Jam Analogy
- In normal metals (like copper wire): Electrons act like cars on a busy highway. They carry both electricity (charge, like cars moving people) and heat (energy, like engine warmth spreading). But drivers constantly bump into each other and road imperfections, creating traffic jams. The more crowded or hotter it gets, the worse the jams – so electricity and heat get blocked together. That’s why the Wiedemann-Franz law holds: charge flow and heat flow rise/fall in lockstep.
- In ultra-clean graphene near the Dirac point: The electrons (and holes) suddenly behave like a coordinated school of fish or a flock of birds. Instead of individual bumping, they move collectively as a fluid, dodging obstacles together with minimal internal friction. Charge can flow one way, while heat flows differently – breaking the old “traffic rule.”
2. Viscosity: Honey vs. Superfluid Helium
- Most fluids are like honey: Thick and sticky (high viscosity). Pour it, and it resists flowing because molecules drag against each other.
- Perfect fluids (Dirac fluid in graphene and QGP) are more like superfluid helium cooled near absolute zero: It flows with zero viscosity – climbing walls, leaking through tiny holes without friction, like a liquid that forgot gravity exists.
Both the Dirac fluid and QGP have viscosity so low they’re among the “most perfect” fluids in nature – flowing effortlessly despite particles smashing into each other trillions of times per second.
3. Visualizing the Systems Themselves
- Graphene’s Dirac fluid: Imagine a flat sheet of carbon atoms where electrons swirl and flow collectively, almost like a frictionless river on a 2D surface.
- Quark-gluon plasma: Picture the aftermath of smashing atomic nuclei at near-light speed – a fireball hotter than the Sun’s core, where protons/neutrons melt into free quarks and gluons, flowing like an ultra-hot, ultra-dense liquid.
Why the Analogy is Powerful
It’s like having a kitchen-table version of the Big Bang’s hottest moments. Scientists can tweak a tiny graphene device at room temperature (or slightly cooled) to study behaviors that normally require massive accelerators like the LHC. This helps understand everything from black hole physics to quantum rules of the Universe – all from a material thinner than paper!
These simple pictures show why physicists are excited: Nature reused the same “perfect flow” recipe in completely different worlds.
