Electron Hydrodynamics in Graphene : Experimental and Theoretical Status

TL;DR

This article surveys electron hydrodynamics in graphene, focusing on the Dirac-fluid regime near the charge neutrality point where electron–electron interactions dominate. It combines experimental signatures such as Poiseuille flow, negative vicinity resistance, and Wiedemann-Franz law violations with a two-branch theoretical framework—non-fluid Fermi-liquid and relativistic Dirac-fluid—to derive thermodynamic and transport coefficients, including an enthalpy-based Lorenz ratio. The Lorenz ratio deviates from the Fermi-liquid value as $L=(\mathfrak{h}/(k_B T))^2 (k_B/e)^2$, consistent with Dirac-fluid behavior, and the computed $\eta/s$ can approach holographic bounds in certain regimes. Overall, graphene is highlighted as a near-perfect electron fluid, providing a bridge between kinetic theory, relativistic hydrodynamics, and mesoscopic transport experiments.

Abstract

The present work comprehensively reviews electron hydrodynamics in graphene, highlighting both experimental observations and theoretical developments. Key experimental signatures such as negative vicinity resistance, Poiseuille flow, and significant violation of the Wiedemann-Franz (WF) law have been discussed, with special emphasis on Lorenz ratio measurements. In the theoretical direction, recent efforts have focused on developing hydrodynamic frameworks for calculating the thermodynamic and transport coefficients of electrons in graphene. The present work has briefly addressed the theoretical framework adopted by our group.

Figures (6)

• Figure 1: The type of charge conduction juxtaposed with that of momentum relaxing and conserving mean free paths.
• Figure 2: Variation of resistance against temperature shown schematically based on gurzhi1963minimumNarozhny_2022.
• Figure 3: (a): Different scattering processes gurzhi1963minimum showing the current profile (b): Phase diagram showing different domains based on scattering process sulpizio2019visualizing.
• Figure 4: Pressure (Left panel) and number density (Right panel) against ($\frac{\mu }{k_B T}$) Dwibedi2025.
• Figure 5: Enthalpy density per particle against ($\frac{\mu }{k_B T}$) Dwibedi2025 (Left panel) and Lorenz ratio vs number density $(n)$ with Experiment-1 PhysRevX.3.041008, Experiment-2 crossno2016observation, Experiment-3 Majumdar2025 and our result Dwibedi2025 (Right panel).