The KPZ equation, introduced in 1986 by physicists Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang, provides a universal description of surface growth phenomena by capturing the intrinsic randomness and nonlinearity inherent in such systems. Its applicability spans from crystal growth and flame propagation to population dynamics and the optimization algorithms driving machine learning. However, experimental confirmation of KPZ universality in two dimensions has long been elusive, primarily due to the formidable challenges of observing and measuring complex, rapidly evolving processes simultaneously in space and time.

The researchers overcame these challenges by engineering a tailor-made gallium arsenide (GaAs) semiconductor device, intricately layered with mirror structures to confine and manipulate polaritons—a peculiar quantum hybrid of photons and excitons. When cooled to near absolute zero temperatures of around −269.15°C and excited with a finely tuned laser pulse, this system produces polaritons which exist fleetingly, decaying within a few picoseconds but exhibiting dynamic growth and interactions that mirror the KPZ framework’s predictions.

By utilizing advanced molecular beam epitaxy, the team achieved atomic-level precision in fabricating their semiconductor sample, controlling the thickness and optical properties of multiple layers to form an ultra-high finesse microcavity. This allowed photons to be trapped and strongly coupled with excitons in the quantum film layer, creating polaritons that exhibit nonequilibrium growth dynamics. Crucially, the researchers developed a method to spatially and temporally map the polariton distributions, generating a high-resolution profile of their evolution over both space and time, thus enabling a direct comparison with the KPZ universality scaling laws.

Siddhartha Dam, a postdoctoral scientist involved in the project, emphasized the experiment’s technical sophistication: “Our ability to track polaritons’ positions with micrometer and picosecond resolution represents an enormous leap forward. Capturing the complex interplay of stochastic growth in two dimensions was previously thought nearly impossible due to the ultrafast nature and microscopic scale of these processes. Our work validates the KPZ equation as a fundamental description of real quantum matter out of equilibrium.”

The theoretical framework underpinning this experiment was proposed by Professor Sebastian Diehl from the University of Cologne, who conceptualized the use of driven polariton quantum fluids as a fertile ground to explore KPZ physics. The 2015 theoretical insights predicted that KPZ scaling could manifest in such nonequilibrium quantum systems, but experimental proof remained out of reach until advances in materials growth and ultrafast optical measurements made the present study possible.

This new experimental realization not only confirms the universality of KPZ scaling in two dimensions but also establishes a platform for exploring a myriad of nonequilibrium quantum phenomena critical for future quantum technologies. Understanding how quantum matter behaves far from thermal equilibrium is fundamental to the development of quantum devices, including sensors, simulators, and potentially quantum computers.

The technical feat hinges on the creation of a polariton condensate confined between carefully engineered mirrors, which reflect light back and forth within the GaAs layer to increase interaction time and enhance measurement sensitivity. The polaritons created are neither purely light nor matter but exhibit hybrid characteristics enabling unique growth dynamics ideal for probing KPZ universality. The researchers could measure how the ‘surface’ formed by the polariton population evolves, from initial fluctuations to the complex spatial correlations that reveal underlying scaling laws.

This breakthrough builds on earlier experimental verifications of the KPZ universality class in one-dimensional settings performed in Paris in 2022. Extending these findings to two spatial dimensions is a monumental step because many real-world growth processes occur in 2D or 3D environments rather than idealized 1D substrates. Demonstrating KPZ scaling for systems with two-dimensional spatial variability charts new territory for non-equilibrium physics.

The implications are profound: by verifying KPZ universality in 2D quantum systems, the work provides physicists and material scientists a vital touchstone for interpreting the behavior of complex, noisy systems. Such insights cut across disciplines, influencing models of epidemic spread, forest fire growth, bacterial colony expansion, and convergence behavior in computational algorithms. KPZ universality effectively serves as a unifying thread tying together diverse phenomena driven by growth and fluctuations.

Researchers employed a suite of cutting-edge measurement techniques, including time-resolved photoluminescence imaging and precise spatial correlation analysis of emitted light as polaritons radiate out of the cavity. These methods revealed the characteristic scaling exponents and height fluctuations predicted by the KPZ equation, providing empirical confirmation that goes far beyond theoretical or numerical models. The towering “spatial correlations” shown in the visualization capture not just static snapshots but the evolving dynamic growth landscape.

Looking forward, the Cluster of Excellence ctd.qmat aims to leverage these findings to probe deeper into quantum matter’s topological and dynamical properties under non-equilibrium conditions. This progress lays the foundational groundwork for the exploration of rich quantum phase transitions and the engineering of novel quantum materials with bespoke properties tuned for next-generation technologies.

In sum, this experimental milestone in demonstrating KPZ universal scaling in two-dimensional systems reconciles decades of theoretical prediction with laboratory reality, opening a window into the unpredictable and fascinating behavior of growing quantum systems. It confirms that the KPZ universality is not merely a mathematical curiosity but a tangible principle governing the evolution of complex natural and artificial worlds alike.

Subject of Research: Not applicable
Article Title: Observation of Kardar-Parisi-Zhang universal scaling in two dimensions
News Publication Date: 9-Apr-2026
Web References: http://dx.doi.org/10.1126/science.aeb4154
Image Credits: © think-design | Jochen Thamm
Keywords: KPZ universality, polaritons, quantum matter, non-equilibrium systems, gallium arsenide, molecular beam epitaxy, two-dimensional scaling, quantum dynamics, surface growth, ultrafast optics, semiconductor microcavity, quantum materials

For decades, physicists have pondered whether electrons could ever behave like an ideal fluid—a state where they collectively move without scattering from impurities or lattice defects, giving rise to frictionless flow properties analogous to superfluids or quark-gluon plasmas. Conventional materials have continually thwarted efforts to observe such behavior due to imperfections that scatter electrons and mask the subtle hydrodynamic effects. However, graphene, with its distinct two-dimensional honeycomb lattice and exceptional electronic properties, has long been regarded as an ideal platform for exploring novel quantum states. Yet, direct evidence of hydrodynamic electron flow behaving as a perfect fluid has remained elusive—until now.

The IISc-led team meticulously prepared and engineered ultra-high-purity graphene samples, eliminating most extrinsic sources of disorder and defects. Using these pristine specimens, they simultaneously measured electrical conductivity—the ease with which electrons carry charge—and thermal conductivity, which reflects the ability of the material to transfer heat via electron motion. Surprisingly, rather than maintaining the well-established proportionality predicted by the Wiedemann-Franz law, their experiments revealed a striking inverse relationship. As the electrical conductivity increased, thermal conductivity decreased dramatically, breaking the long-held principle that heat and charge conductance should scale hand-in-hand in metals.

This profound violation of the Wiedemann-Franz law by more than two hundredfold at low temperatures signals the emergence of a unique quantum liquid regime. At the heart of this behavior is the so-called Dirac point, where graphene’s electronic band structure yields massless charge carriers and where electrons neither conform to metallic nor insulating states. Near this point, electrons abandon their typical particle-like individuality and instead coalesce into a collective “Dirac fluid.” This fluid flows similarly to water but displays quantum effects such as minimal viscosity—far lower than any classical fluid—thus qualifying it as the closest experimental realization of a perfect quantum fluid in a solid.

The researchers explain that, in the Dirac fluid regime, both charge and heat transport depend on a universal quantum of conductance—a fundamental constant describing the minimal resistance electrons experience when flowing across materials. This universality highlights the exotic nature of electron interactions within graphene, governed more by intrinsic quantum critical phenomena than by material-specific imperfections. Consequently, electrical and thermal conduction processes decouple fundamentally, invalidating traditional conductivity models that treat electrons as largely independent carriers.

To characterize the fluidity quantitatively, the team measured the fluid’s viscosity—a parameter indicating internal friction opposing flow. Their results revealed an extraordinarily low viscosity, on par with other strongly correlated quantum systems such as the quark-gluon plasma observed in ultra-high-energy collisions at CERN’s Large Hadron Collider. Such correspondence suggests that the graphene Dirac fluid can serve as a low-energy table-top analog to explore extreme quantum states usually accessible only in particle physics experiments and astrophysical scenarios.

Beyond its fundamental importance, this discovery positions graphene as an unparalleled quantum laboratory for investigating rich phenomena like black-hole thermodynamics and entanglement entropy scaling, concepts that historically belong to the realms of cosmology and quantum information theory. The ability to simulate and probe these exotic states in a controlled laboratory environment will undoubtedly accelerate progress across condensed matter physics and quantum technologies.

Technological implications of this research are equally profound. The emergence of a quantum perfect fluid phase in graphene paves the way for quantum sensors engineered to exploit the decoupling of charge and heat flows, granting these devices heightened sensitivity. Potential applications include amplification of weak electrical signals and detection of minute magnetic fields, advancing fields such as quantum metrology and medical imaging.

Professor Arindam Ghosh of IISc, one of the study’s senior authors, emphasizes the enduring richness of graphene’s physics despite two decades of intense scrutiny. “It is amazing that there is so much to do on just a single layer of graphene even after 20 years of discovery,” he notes, underscoring the material’s continual capacity to surprise and inspire.

First author Aniket Majumdar explains that this work marks a key milestone in realizing a Dirac fluid state experimentally. He points out that this unique electronic phase is “an exotic state of matter which mimics the quark-gluon plasma,” highlighting its importance in bridging condensed matter and high-energy physics. The study’s observation that electron flow near the Dirac point mimics such a nearly perfect fluid feeds into longstanding theoretical predictions regarding quantum criticality and hydrodynamic transport in two-dimensional materials.

The team’s approach involved precise tuning of graphene’s carrier density to reach the Dirac point through electrostatic gating techniques, enabling unprecedented control over the electron fluid’s properties. By cooling the samples to cryogenic temperatures, they suppressed extrinsic thermal scattering and unveiled intrinsic collective electron phenomena that remain hidden at higher energies.

Their findings demonstrate a new universality class of quantum critical flow, distinct from classical or previously known quantum transport regimes. This universality is characterized by the reliance on fundamental constants governing conductance rather than sample-specific parameters, reinforcing graphene’s status as a model system to study quantum fluids with direct experimental accessibility.

As a result, the IISc team’s breakthrough establishes a vibrant new frontier in quantum materials research. By taking quantum fluid dynamics out of particle accelerators and astrophysics labs and placing it squarely in a table-top graphene device, this study promises to reshape fundamental physics paradigms and to spark technological innovations exploiting quantum hydrodynamics in future nanoelectronic systems.

The research is published in the prestigious journal Nature Physics, amplifying its impact and signaling global recognition for this milestone achievement. This advance in understanding electron behavior at the quantum critical point in graphene not only enriches our fundamental knowledge of quantum many-body systems but also energizes diverse areas of physics—ranging from condensed matter to quantum information and high-energy theory.

As materials science continues to push boundaries, discoveries such as this spotlight the profound possibilities emerging from atomically thin materials. Graphene’s exceptional electron fluidity offers a glimpse into an extraordinary quantum world, where electrons flow as a near-perfect liquid, setting the stage for innovations that transcend conventional electronics and unveil unexplored quantum frontiers.

Subject of Research: Quantum fluid behavior of electrons in ultraclean graphene

Article Title: Universality in quantum critical flow of charge and heat in ultraclean graphene

News Publication Date: 13-Aug-2025

Web References:
https://www.nature.com/articles/s41567-025-02972-z
http://dx.doi.org/10.1038/s41567-025-02972-z

Image Credits: Aniket Majumdar

Keywords

Graphene, quantum fluid, Dirac fluid, electron hydrodynamics, quantum criticality, Wiedemann-Franz law violation, quantum conductance, minimal viscosity, quantum transport, graphene electronics, ultraclean graphene, quantum sensors