Rayleigh-Bénard Instability in Graphene
arXiv:1410.8177 · doi:10.1103/PhysRevB.91.085401
Abstract
Motivated by the observation that electrons in graphene, in the hydrodynamic regime of transport, can be treated as a two-dimensional ultra-relativistic gas with very low shear viscosity, we examine the existence of the Rayleigh-Bénard instability in a massless electron-hole plasma. Firstly, we perform a linear stability analysis, derive the leading contributions to the relativistic Rayleigh number, and calculate the critical value above which the instability develops. By replacing typical values for graphene, such as thermal conductivity, shear viscosity, temperature, and sample sizes, we find that the instability might be experimentally observed in the near future. Additionally, we have performed simulations for vanishing reduced chemical potential and compare the measured critical Rayleigh number with the theoretical prediction, finding good agreement.
arXiv comment10 pages, 9 figures
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- Lattice Boltzmann method for semiclassical fluids
- Fully dissipative relativistic lattice Boltzmann method in two dimensions
- Numerical evidence of electron hydrodynamic whirlpools in graphene samples
- Strong suppression of electron convection in Dirac and Weyl semimetals
- Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
- Thermal dissipation in two dimensional relativistic Fermi gases with a relaxation time model
- Two Dimensional Turbulence in a Massless Fluid with a Relativistic Lattice Boltzmann Model
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