Temperature dependence of electron-fluid viscosity

Determine the exact functional form of the temperature dependence of the kinematic shear viscosity ν(T) in hydrodynamic electron systems, particularly in graphene, resolving whether ν(T) follows a T^{-2}, T^{-1}, or other scaling across relevant parameter ranges.

Background

Viscosity controls a wide range of hydrodynamic transport phenomena, but extracting it experimentally is challenging because viscous and momentum-relaxing contributions are intertwined. Fermi-liquid theory predicts ν ∝ T{-2} in 3D (with tomographic modifications possible in 2D), whereas reported experimental trends vary. Clarifying ν(T) is essential for quantitative hydrodynamic modeling and for interpreting signatures such as Gurzhi behavior and width scaling.

References

Measured viscosities generally decrease with temperature, but the exact functional form is still unknown; depending on the experiment, the temperature dependence can range from ν ∝ T{-2} to ν ∝ T{-1} (see Fig.~\ref{fig: mlg viscosity vs temp}).

— Hydrodynamics of the electronic Fermi liquid: a pedagogical overview (2504.01249 - Hui et al., 1 Apr 2025) in Section “Viscosity” (subsection of Fermi Liquid Hydrodynamics)