Electronic hydrodynamics in graphene

Abstract

Highlights: Electrons in ultra-clean graphene at high enough temperatures behave hydrodynamically. Unconventional hydrodynamics in graphene can be derived from the kinetic theory. Kinetic coefficients include the quantum conductivity and shear and Hall viscosities. -- Abstract: In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations cannot be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resulting theory with relativistic hydrodynamics.