Electron viscosity from first principles: from graphene to anisotropic Fermi surfaces

In ultra-pure materials at low temperature, electron-electron (e-e) interactions become the dominant scattering mechanism, and the electrons enter the hydrodynamic regime where the they experience viscous flow. Motivated by the possible development of electronic analogues of turbulence and vorticity, the hydrodynamic regime promises exciting opportunities for quantum technologies. Recent work in this field has focused on doped graphene, a system with a circular Fermi surface where viscous transport can be described using simple models from kinetic gas theory. However, these models are not easily extended to other 2D materials, most of which do not have circular Fermi surfaces. In this talk, we present a first-principles theory of electron viscosity in the framework of the Boltzmann transport equation. Our treatment, which parallels more established calculations of electron-phonon dominated transport, provides theory and computational workflows to calculate the viscosity in the relaxation-time approximation and beyond. Within this framework, we study the e-e interactions and electron viscosity in doped graphene and other 2D materials, determining the effects of the anisotropy of the Fermi surface on the viscosity tensor and on hydrodynamic transport phenomena. Together, these developments pave the way for microscopic understanding of viscous transport in real materials.