Weyl hydrodynamics in a strong magnetic field

We study the hydrodynamic transport of electrons in a Weyl semimetal in a strong magnetic field. Impurity scattering in a Weyl semimetal with two Weyl nodes is strongly anisotropic as a function of the direction of the field and is significantly suppressed if the field is perpendicular to the separation between the nodes in momentum space. This allows for convenient access to the hydrodynamic regime of transport, in which electron scattering is dominated by interactions rather than by impurities. In a strong magnetic field, electrons move predominantly parallel to the direction of the field, and the flow of the electron liquid in a Weyl-semimetal junction resembles the Poiseuille flow of a liquid in a pipe. We compute the viscosity of the Weyl liquid microscopically and find that it weakly depends on the magnetic field and has the temperature dependence $\eta(T)\propto T^2$. The hydrodynamic flow of the Weyl liquid can be generated by a temperature gradient. The hydrodynamic regime in a Weyl-semimetal junction can be probed via the thermal conductance $G_q(B,T)\propto B^2 T$ of the junction.
Comment: 15 pages, 3 figures