Dirac fluid in graphene: basic physics for new energy

By Neutrino Energy 7 May 2026

Dirac fluid in graphene: basic physics for new energy

Breakthrough of the Dirac fluid:

What electron transport in graphene means for neutrinovoltaic technology

In April 2026, a study was described in which a joint research team from Japan and India observed extraordinary transport behaviour in extremely pure graphene: electrons did not move like independent particles but like an almost frictionless quantum fluid. Particularly remarkable is that electrical conductivity and thermal conductivity did not rise together as in classic metals, but in some cases behaved in opposite directions. This behaviour clearly contradicts the classic Wiedemann–Franz law and opens up a new view of energy and charge transport in two-dimensional materials. For neutrinovoltaic technology, this observation is of particular importance. Its technological core consists in not considering weak quantised energy and momentum transfers from the environment as individual isolated events, but in statistically integrating them in nanostructured materials and making them electrically usable. Graphene, especially in the state of a Dirac fluid, offers a physically interesting platform for this, because collective electron motion, low losses and a possible decoupling of heat and charge transport are central prerequisites for such energy integrators.

When quantum materials challenge classic transport laws

In classic metals, electric charge and heat are usually carried by the same charge carriers. This results in a close relationship between electrical conductivity and thermal conductivity, known since the 19th century as the Wiedemann–Franz law. Put simply, it states: a material that conducts electricity very well usually also conducts heat very well.

For many metallic materials this rule is extremely successful. It is based on the idea that electrons act as relatively independent particles and transport both charge and energy according to similar scattering mechanisms. Graphene, however, shows that this classic view is not always sufficient. In certain states, especially close to the charge neutrality point, the electrons no longer behave like an ordinary electron gas. Instead, a collective state arises that is called a Dirac fluid.

Motion is determined less by individual particle paths than by collective interactions.

In this state, electrons and holes can flow together like a liquid. Motion is then determined less by individual particle paths than by collective interactions. It is precisely this property that makes graphene interesting for new concepts of energy conversion. If microscopic energy impulses are not immediately lost as heat but can be transferred into collective electronic motion, a possible path opens up to the technical use of very weak momentum and energy flows.

Wiedemann–Franz law

\frac{κ}{σ} = L T

Sommerfeld value of the Lorenz number

L_{0} \approx 2.44 \times 10^{-8}

Graphene and the Dirac fluid

Graphene consists of a single layer of carbon atoms arranged in a hexagonal lattice. This seemingly simple structure leads to extraordinary electronic properties. Near the so-called Dirac points, electrons in graphene behave as if they had no effective mass. There, their energy depends approximately linearly on momentum. That is why they are called Dirac fermions.

At the charge neutrality point, the number of free charge carriers is very small. At the same time, disturbances caused by impurities and lattice vibrations can be greatly reduced in very pure samples. Under such conditions, the interaction of the electrons with each other dominates. The system leaves the classic regime of a Fermi liquid and enters a quantum fluid state. This state is the Dirac fluid.

The Dirac fluid is so relevant because it forms a bridge between solid-state physics, quantum hydrodynamics and energy conversion. It shows that charge carriers in a solid do not necessarily have to be regarded as independent particles. Under suitable conditions, they behave like a collective medium that can pass on momentum and energy in a coordinated way over larger distances.

Linear dispersion in graphene

E = \pm v_{F} ℏ | k |

Fermi velocity in graphene

v_{F} \approx 1 \times 10^{6}

Density of states near the Dirac point

ρ (E) \propto | E |

Plasmon frequency at low carrier density

ω_{p} \propto \sqrt{n}

Superballistic transport: when collective motion exceeds the limits of single particles

In ordinary nanoscale conductors there is a natural limit to electrical transport. This limit is related to the conductance quantum. If a channel becomes so small that electrons cross it almost without scattering, this is called ballistic transport. In the Dirac fluid, however, an even more unusual state can occur: superballistic transport.

Superballistic transport means that the collective motion of the electrons improves effective transport, even though individual particles continue to interact with the edges or with each other. The electrons then act not like isolated particles but like a viscous fluid. This fluid can partly compensate for edge losses and thus enable a higher conductance than expected in a simple single-particle picture.

For energy integrators based on nanostructured materials, this is an important indication. The technical challenge is not only to absorb microscopic energy impulses, but to convert them into directed electrical motion with low losses. A collective transport state such as the Dirac fluid can be a particularly suitable platform for this.

Conductance quantum

G_{0} = \frac{2 e^{2}}{h}

Observed superballistic conductance

G \approx 1.2 - 1.5 G_{0}

The violation of the Wiedemann–Franz law

The observed decoupling of heat and charge transport is particularly significant. According to classic expectations, increasing electrical conductivity should also be associated with increasing electronic thermal conductivity. In the Dirac fluid of graphene, however, the opposite can occur: electrical conductivity rises while thermal conductivity falls.

The reason lies in the special structure of the Dirac fluid. Electrons and holes can carry energy and charge in different ways. At the Dirac point, energy flow can be determined partly by co-directional motion of electron-hole pairs, while the net electric current is independently influenced by an external field. This makes it possible to separate charge flow and energy flow physically.

For neutrinovoltaics this property is central. An ideal nanostructured energy integrator should transport electric charge efficiently without immediately losing the absorbed energy as heat. Precisely this combination of high electrical conductivity and reduced heat conduction corresponds to the technical aim: not maximum heat spreading, but directed electrical transduction.

Reduced ratio of electronic thermal conductivity to electrical conductivity

\frac{κ_{e}}{σ} \approx 0.8 \times 10^{-8}

Opposite development of conductivity and thermal conductivity

σ ↑, κ ↓

Neutrinovoltaics as an integrator for nanostructured energy

Neutrinovoltaic technology is often misunderstood when it is described in abbreviated form as the direct “conversion of neutrinos into electricity”. It is more precisely described as a nanostructured energy integrator. What is meant is a material system that absorbs weak quantised momentum and energy transfers from the environment, statistically sums them over many active interfaces and converts them into measurable electrical signals via suitable electronic structures.

Neutrinos can transfer momentum to matter via coherent elastic neutrino-nucleus scattering, CEνNS for short. In this process, a neutrino scatters elastically off an atomic nucleus without destroying it or causing a charge conversion. The individual energy transfer is extremely small, but physically real. What matters, therefore, is not the individual event, but whether a suitable material system can absorb, couple and electrically integrate very many of these weak impulses.

Graphene-based heterostructures are interesting for such concepts because they offer a high density of interfaces, exceptional electronic mobility and strong coupling to collective excitations such as phonons, plasmons and Dirac fluid modes. Neutrinovoltaics therefore does not stand outside known physics, but combines known interactions with nanostructured conversion mechanisms.

The Schubart master equation: the phenomenological framework

The so-called Schubart master equation describes neutrinovoltaic technology as a phenomenological model of energy integration. It is not meant to replace the standard theory of particle physics, but to bring together the factors relevant to a technical material system: the effective particle flux, the energy-dependent cross-section, the active volume and the conversion efficiency of the material.

In general notation, the equation describes the electrical output power as a product or integral of ambient flux, effective interaction and usable conversion volume. The decisive point is that the power does not arise from a single event but from the sum of many microscopic contributions. This is precisely where it resembles the concept of the Dirac fluid: there too, transport is no longer dominated by individual isolated particles but by collective motion.

The Schubart master equation in general form

P (t) = η \int_{V} Φ_{a m b} (r, t) σ_{e f f} (E) d V

Here P(t) stands for the electrical output power, η for the material- and structure-dependent conversion efficiency, Φamb for the effective ambient flux of relevant particles or momentum sources, σeff for the effective cross-section and ⟨Etr⟩ for the energy usefully transferred in the material.

Important: this equation is a technical balance model. It does not replace a quantum field theory calculation, but orders the parameters relevant to energy conversion from experimental and materials-physics perspectives.

CEνNS: coherent elastic neutrino-nucleus scattering

Coherent elastic neutrino-nucleus scattering is a central physical anchor of neutrinovoltaics. Coherence here means that the neutrino does not scatter off a single nucleon only, but that the atomic nucleus as a whole takes part in the scattering. As a result, the scattering amplitudes of many nucleons can add up. The effective cross-section grows approximately with the square of the number of neutrons or nucleons.

Although the interaction remains weak, this coherent enhancement effect is important. It shows that neutrinos can in principle transfer measurable momentum and measurable energy to matter. For a technical system, the materials question is then decisive: how can this extremely small momentum be converted into lattice vibrations, collective electronic states and finally directed charge transport?

Coherence condition

λ_{ν} > R

Coherent enhancement of the cross-section

σ \propto N^{2}

From microscopic momentum to electrical signal

A single neutrino scattering impulse is extremely small. In a classic macroscopic material, such an effect would practically vanish immediately in the thermal noise. In a nanostructured heterostructure, the situation can be assessed differently. There are very many interfaces, quantised vibration modes and electronic asymmetries there that can absorb and process weak impulses.

The physical path can be described in simplified terms as follows: a weak impulse creates a local lattice vibration or modifies an existing quantised vibration mode. This excitation couples to electrons in graphene or related two-dimensional materials. If the structure is asymmetric – for example through doping, p-n junctions, p-i-n junctions or nanoscale rectifiers – directed charge transport can result.

The Dirac fluid is particularly interesting in this context because it does not just dissipate microscopic impulses locally but allows collective states of motion. Such states can act as a mediating medium that distributes weak excitations over larger electronic contexts and thus increases the probability of a measurable electrical response.

Order of magnitude of a single energy transfer

E \sim 10^{-10}

Example of local amplification

A \sim 32

Terahertz excitations and rectification

Many of the relevant lattice vibrations and collective excitations in nanoscale materials lie in the terahertz range. A technical challenge is therefore to convert these very fast alternating movements into a directed direct current. This requires asymmetric nanostructures, fast rectifiers and suitable material combinations.

The connection to neutrinovoltaics is that energy integration does not end with the creation of a vibration. Only coupling to electronic asymmetries and rectification mechanisms turns a weak quantised excitation into a usable electrical signal. In this respect, graphene transport, nano-interfaces and rectifier physics complement each other.

Rectification ratio as an example quantity

R \approx 120

Example laboratory efficiency

η \approx 26.3 %

Why the Dirac fluid experiments matter for neutrinovoltaics

The Dirac fluid experiments do not directly confirm a finished neutrinovoltaic cell, but they do confirm several material prerequisites that are decisive for such a technology:

First, they show that graphene, within a suitable range of purity and temperature, can enable collective, low-loss electron transport.
Second, they show that electrical conductivity and heat conduction do not necessarily have to increase together.
Third, they provide measurable parameters for quantum hydrodynamic modelling of such systems.

This is significant for technical development because it makes a central assumption more plausible: a nanostructured material can not only absorb weak energy inputs, but convert them into directed electrical processes via collective electron dynamics. The decisive question thus shifts from the mere existence of microscopic energy transfer to the efficiency of its coupling, integration and rectification.

In other words: neutrinovoltaics does not claim that neutrinos suddenly deliver large amounts of energy per single event. What matters instead is that a large number of weak impulses can be statistically summed in a suitable material system and made electrically usable through nanoscale transport mechanisms. The Dirac fluid provides an important physical model for exactly this.

Quantum viscosity: the almost perfect fluid as a transport medium

Another important aspect is viscosity. In classic liquids, viscosity describes the internal resistance to flow. In an electron fluid there is a comparable quantity: it describes how strongly the collective motion of the electrons dissipates internally. A very low effective viscosity means that momentum can be transferred efficiently through the electron system.

For an energy integrator this is decisive. Microscopic impulses should not immediately turn into disordered heat but be translated as orderly as possible into electrical motion. An almost perfect quantum fluid offers a particularly favourable transport medium for this. It allows a more coherent transfer of momentum and reduces the probability that the absorbed energy disappears prematurely as thermal loss.

From a phenomenological model to quantitative development

For its further development, neutrinovoltaic technology needs not only qualitative plausibility but quantitative material parameters. This is exactly where Dirac fluid experiments are particularly valuable. They provide values for conductivity, thermal conductivity, viscosity, temperature dependencies and transport regimes. Such data can feed into technical balance models such as the Schubart master equation.

This allows development to move from a purely phenomenological description to stricter modelling based on measured values. What matters is not only particle flux and cross-section, but also the material response: how strongly does an impulse couple to the lattice? How efficiently does an electronic excitation result? How large is the rectification? And what losses occur through heat conduction, defects or recombination?

Outlook: material optimisation and technical integration

The next development steps lie above all in material and structural control. Graphene must be produced in high purity and with a suitable interface architecture. Heterostructures of graphene, silicon, hexagonal boron nitride and other two-dimensional materials could be used to specifically improve charge separation, phonon coupling and rectification.

Another goal is miniaturisation. Compact energy integrator modules are conceivable in which conversion, rectification, intermediate storage and voltage stabilisation are integrated in a chip or layer system. Such systems would be particularly interesting for applications that require very low but continuous power: sensors, IoT nodes, underwater technology, space travel, medical microsystems or shielded environments.

At the same time, fundamental physics remains essential. Methods such as ARPES, STM and ultrafast spectroscopy can help to better understand the microscopic dynamics of the Dirac fluid. Topological Dirac materials, moiré superlattices and other two-dimensional heterostructures could also provide new platforms for integrating weak energy flows in future.

Target value for theoretical conversion efficiency

η \approx 22 %

Conclusion:

The observation of the Dirac fluid in high-purity graphene represents an important step in understanding collective quantum transport processes. It shows that classic transport laws such as the Wiedemann–Franz law can lose their validity in strongly correlated two-dimensional systems. Electric charge and heat do not necessarily have to be transported together. Under suitable conditions, a material can combine high electrical conductivity with reduced heat conduction.

For neutrinovoltaic technology, this is of great importance. It is not based on the idea of generating energy from nothing, but on integrating weak quantised momentum and energy flows in nanostructured energy converters. The Dirac fluid provides a strong physical reference model for this: collective transport, low dissipation, thermal-electrical decoupling and quantum hydrodynamic describability.

This creates a more consistent picture of neutrinovoltaics as an energy integrator at the quantum level. The central task of the coming years is to develop the experimentally observed mechanisms of quantum transport into robust, scalable and technically reproducible components.

Neutrinovoltaics – Dirac fluid with claim