Strong suppression of electron convection in Dirac and Weyl semimetals

It is shown that the convective instability in electron fluids in three- and two-dimensional (3D and 2D) Dirac and Weyl semimetals is strongly inhibited. The major obstacles for electron convection are the effects of the Coulomb forces and the momentum relaxation related to the interaction with impurities and phonons. The effect of the Coulomb forces is less pronounced in 2D materials, such as graphene. However, momentum relaxation still noticeably inhibits convection, making it very difficult to achieve in practice.

Figure 1

Solid lines show the minimal Rayleigh number needed for convection. The realistic Rayleigh numbers achievable in Dirac semimetals are shown by the shaded regions. Dashed lines show the Rayleigh number (24) calculated for $\delta T=T_0$ and $\tilde{E}=10\mathrm{V}/\mathrm{m}$. The Gurzhi length is ${\lambda }_G\approx 0.4\mu \text{m}$ and the values of the Thomas-Fermi wave vector are $q_{\mathrm{TF}}\approx 2\times {10}^6{\text{cm}}^{-1}$ at ${\mu }_0=1\text{meV}, q_{\mathrm{TF}}\approx 5.2\times {10}^6{\text{cm}}^{-1}$ at ${\mu }_0=10\text{meV}$, and $q_{\mathrm{TF}}\approx 2.4\times {10}^7{\text{cm}}^{-1}$ at ${\mu }_0=50\text{meV}$.