Researchers are increasingly investigating the potential for hydrodynamic electron behaviour in high-mobility graphene, aiming to replicate relativistic fluid dynamics within solid-state devices. Richa P. Madhogaria, Aniket Majumdar, and colleagues from the Department of Physics, Indian Institute of Science, Bangalore, in collaboration with Kenji Watanabe and Takashi Taniguchi at the National Institute for Materials Science in Japan, have explored electron viscosity and its variability in ultra-clean graphene field-effect transistors. This study, also involving researchers from the Center for Nano Science and Engineering at the Indian Institute of Science, addresses a critical challenge in the field, the significant device-dependent variations observed in experiments designed to detect electron hydrodynamics. By employing a simple four-terminal device architecture and detailed electrical transport measurements, the team reveals that these variations stem from a complex interplay of momentum-conserving and momentum-relaxing scattering mechanisms, alongside contact coupling, offering a new phenomenological method for accurately extracting viscous electron contributions in advanced graphene devices.

Can electrons flow like a fluid in solid materials, exhibiting viscosity similar to water. Measurements in ultra-clean graphene now demonstrate that this behaviour is surprisingly sensitive to how the electronic device is made. Understanding this variability is essential for building future electronic components based on these unusual electron flows. Scientists are increasingly focused on understanding how electrons behave as fluids, a concept with potential to revolutionise electronics.

Recent work explores the possibility of creating an electronic analogue of a relativistic quantum fluid within solid materials, specifically utilising the unique properties of graphene. Upon observing this ‘electron hydrodynamics’ requires electrons to travel long distances without losing momentum, a condition hampered by imperfections and atomic vibrations within the graphene itself.

For over a decade, researchers have attempted to overcome these limitations through complex device designs, yet experimental results often appear inconsistent, raising doubts about whether observed effects genuinely represent hydrodynamic behaviour. Now, a new study presents findings from a series of ultra-clean graphene field-effect transistors (FETs) constructed with a simple, rectangular four-terminal architecture.

Electrical transport measurements were performed to assess the quality of the graphene and examine how electrical resistance changes with both the number of charge carriers and temperature. Outcomes indicate substantial variation between devices, even with this simplified design, suggesting that multiple scattering processes are at play alongside the influence of the electrical contacts.

This variability isn’t simply noise; instead, it appears linked to competing mechanisms that either preserve or disrupt electron momentum. Scientists have developed a new analytical method to interpret these results, yielding transport parameters consistent with previous experiments. This streamlined approach offers a valuable tool for isolating and quantifying the viscous flow of electrons in advanced graphene FETs. Potentially paving the way for novel electronic devices.

At the core of this investigation lies the challenge of achieving a long ‘momentum-relaxation path’ for electrons. In graphene, this path is typically limited by collisions with impurities or atomic vibrations, known as phonons. While complex device geometries have been used to minimise these collisions, researchers have used these geometries to minimise these collisions.

By employing a simple device structure and focusing on ultra-clean graphene samples, this project aims to provide a clearer picture of the underlying physics — also, the proposed analytical method offers a means to disentangle the contributions of different scattering mechanisms and contact effects. Here, this is particularly important because the behaviour of electrons near the ‘Dirac point’, where the conduction and valence bands meet, and is expected to be different from that at higher carrier densities. Understanding these variations is essential for accurately modelling and predicting the performance of graphene-based electronic devices.

Observed resistance and conductivity variations in graphene devices at varying carrier densities and temperatures

Electrical resistance measurements across multiple graphene devices reveal substantial variation, even within a simple four-terminal architecture. Initial analysis of four-probe resistance (R4p) versus carrier density demonstrates differences between devices, with values ranging widely at 100 K. Device D3S4 exhibited a resistance of 1.2 kΩ at a carrier density of 1x 10¹² cm⁻². Meanwhile, D1S5 showed 0.3 kΩ at the same density.

Normalized electrical conductivity measurements further highlight these discrepancies; at a carrier density of 4x 10¹¹ cm⁻², devices D1S5, D3S5 — D5S5 displayed conductivity values differing by as much as 20%. Examination of resistance as a function of temperature reveals additional complexity. At intermediate and high densities, devices D3S4, D3S5. D1S4 all showed a decrease in R4p with increasing temperature, though the rate of decrease varied.

Specifically, D3S4 maintained a resistance above 0 Ω across the measured temperature range — whereas D3S5 and D1S4 both exhibited negative resistance regions at higher temperatures. Correlating R4p with total charge inhomogeneity (nmin) at 100 K and a carrier density of 4x 10¹¹ cm⁻² provides further insight, and at this specific condition, devices D3S4 and D1S4 showed minimal resistance, near 0 Ω. Meanwhile, D3S5 registered a markedly higher value.

Inside the devices, electron mobilities ranged between 10⁵ and 10⁶ cm²V⁻¹s⁻¹ at 240 K. Mean free paths exceeded 1μm at all temperatures. Through analysis of R4p against temperature at a carrier density of 5x 10¹¹ cm⁻², a consistent trend of decreasing resistance with increasing temperature was observed across all devices. Though the magnitude of the change differed. These competing momentum-conserving and momentum-relaxing scattering mechanisms, alongside contact coupling, contribute to the observed device-dependent variability.

High-mobility graphene heterostructure fabrication and low-temperature transport characterisation

Electrical transport measurements across ultra-clean graphene field-effect transistors (FETs) underpinned this effort, allowing detailed characterisation of material quality and electrical behaviour. Specifically, researchers performed four-terminal measurements on rectangular graphene devices encapsulated within hexagonal boron nitride (hBN) to minimise scattering from the substrate and environmental impurities.

These hBN-encapsulated heterostructures were fabricated to achieve high electron mobilities, ranging from 105 to 106 cm2V−1s−1 at 240 K, and extended mean free paths. Once fabricated, electrical contacts were patterned using electron-beam lithography and deposited via a combination of titanium and gold, ensuring low-resistance connections to the graphene channel.

Then, devices underwent thorough characterisation to assess their electrical properties as a function of carrier density and temperature. By applying gate voltages, the carrier density within the graphene channel was precisely tuned. Systematic investigation of the material’s response across a range of doping levels. In turn, at each carrier density, researchers measured the four-probe resistance over a temperature range, providing insights into the dominant scattering mechanisms.

Through acknowledging potential variations between devices, multiple samples were fabricated and measured to establish a statistically relevant dataset. To account for contact contributions to the overall resistance, researchers chose a four-probe configuration over two-probe measurements, providing a more accurate assessment of the intrinsic graphene channel resistance.

Beyond standard measurements, a phenomenological method was developed for analysing the collected data, yielding key transport parameters consistent with recent findings in the field. At the same time, this analysis allowed extraction of the total charge inhomogeneity, a parameter vital for understanding the interaction between momentum-conserving and momentum-relaxing scattering processes.

Instead of complex device geometries, a simple rectangular architecture was deliberately selected to minimise fabrication-induced artefacts and focus on intrinsic material properties. Through employing this streamlined approach, The project aimed to establish a clear baseline for identifying genuine signatures of electron hydrodynamics, free from the confounding effects of complex device layouts.

Graphene transistor inconsistencies obscure evidence for electron fluid behaviour

Scientists pursuing the elusive goal of fluid-like electron behaviour in solids have long faced a frustrating paradox. While theory predicts a smooth, viscous flow under specific conditions, replicating this in actual materials proves remarkably difficult. Recent work with graphene, a two-dimensional material celebrated for its electron mobility, offers a step forward. But also a sharp reminder of the challenges involved in isolating genuine hydrodynamic effects from background noise.

The presented research focuses on carefully fabricated graphene transistors, aiming to establish a clearer picture of electron flow. Outcomes reveal a persistent problem: considerable variation between devices, even those built to the same specifications. In turn, this suggests that subtle imperfections, or variations in contact coupling, can overwhelm the delicate signature of hydrodynamic transport.

Instead of a clear, universal signal, researchers encounter a complex mix of behaviours, where electrons sometimes behave as expected. Meanwhile, at other times scatter more conventionally. A new analytical method is proposed to disentangle these competing influences, providing a means to extract the viscous component from the overall electrical signal. Extracting meaningful parameters from these experiments demands careful consideration of the underlying assumptions.

The proposed model, while aligning with existing data, relies on a phenomenological approach. It describes how things happen rather than why. Unlike more fundamental theories, it doesn’t fully explain the microscopic mechanisms driving the observed behaviour. For years, the field has been limited by the difficulty of creating sufficiently pristine samples and controlling external factors.

Once these hurdles are addressed, the potential is considerable. Beyond fundamental physics, understanding electron hydrodynamics could unlock new avenues for designing ultra-low power electronics — by manipulating electron flow at the nanoscale, it may be possible to create devices that dissipate minimal energy. Future work must focus on refining fabrication techniques and developing more sophisticated theoretical models to truly understand and control this fascinating phenomenon, and beyond graphene, exploring similar effects in other two-dimensional materials could broaden the scope of this project and reveal new possibilities for electronic design.

👉 More information
🗞 Electron viscosity and device-dependent variability in four-probe electrical transport in ultra-clean graphene field-effect transistors
🧠 ArXiv: https://arxiv.org/abs/2602.16847