Relationship between Boltzmann-derived and two-mode hydrodynamic formulations near charge neutrality

Ascertain how the hydrodynamic equations for graphene near charge neutrality obtained from the Boltzmann equation compare to those from a two-mode decomposition that treats the zero-momentum mode ohmically and the finite-momentum mode via a Stokes equation, and determine the regimes in which the two approaches agree or differ.

Background

Near charge neutrality in graphene, two frameworks are used: (i) deriving hydrodynamics from the Boltzmann equation, and (ii) a phenomenological two-mode approach that couples a zero-momentum (ohmic) mode with a finite-momentum (Stokes) mode. While both aim to capture electron–hole plasma hydrodynamics, their quantitative equivalence and domain of validity have not been established.

References

This approach results in slightly different equations of motion as compared to constructing hydrodynamics from the Boltzmann equation and then taking the appropriate limits. At the time of writing, it is unclear to the authors how similar or distinct these two approaches are.

— Hydrodynamics of the electronic Fermi liquid: a pedagogical overview  (2504.01249 - Hui et al., 1 Apr 2025) in Section “Electron-Hole and Dirac Fluid Hydrodynamics” (subsection of Beyond Isotropic Fermi Liquid Hydrodynamics)

Since a complete expression for this boundary term throughout the Stokes--Ohm crossover is not presently available, we do not introduce it as an additional fitting parameter.

— Hydrodynamic magnetotransport in a GaAs Corbino geometry  (2609.10511 - Levin et al., 9 Sep 2026) in Section 3, Theoretical model, immediately following Eq. (12) (with the same issue discussed in Section 4, Discussion and comparison with experiment)