Transport properties of charged two-dimensional Dirac systems in hydrodynamic regime: the role of dynamical screening and plasmons

Clean two-dimensional Dirac systems, for example, graphene, have received a lot of attention for being a prime candidate to observe hydrodynamical transport behavior in interacting electronic systems. In this work, we investigate the role of dynamical screening effect which gives rise to a collective mode, called plasmon, in the thermo-electric transport properties of those systems. We find that the plasmon is an additional low-energy degree of freedom which makes a sizeable contribution to thermal conductivity and shear viscosity of graphene. We propose a novel type of hydrodynamics consisting of electrons, holes, and plasmons. We find that the form of the hydrodynamic equations as well as the definition of conserved quantities are not only constrained by symmetries of the kinetic energy but also by the interactions of the underlying system. Our result suggests that this is a generic feature of ultraclean two-dimensional electronic systems, also applicable to 2DEL, Bernal-stacked and twisted bilayer graphene.