Intrinsic Plasmon damping in Dirac-Fermi liquids

A Dirac-Fermi liquid (DFL) —a doped system with Dirac spectrum—is a special and important subclass of non-Galilean-invariant Fermi liquids (FLs), which includes, e.g., monolayer graphene and surface states of three-dimensional topological insulators. The lack of Galilean invariance leads to some interesting features not encountered in conventional Fermi liquids. Namely, the dissipative part of the conductivity of a DFL stays finite at q→0, whereas for a Galilean-invariant FL it vanishes as q². We explore the consequences of this fundamental difference for the intrinsic damping of plasmons in DFL. Charge density fluctuation leads to a collective mode, plasmon, in a two-dimensional (2D) system with q^1/2 dispersion. The imaginary part of charge susceptibility, χ''(q, ω), is directly related to the damping rate of the plasmon mode. We obtain the explicit form of χ''(q, ω) for DFL, by going beyond the random-phase approximation. We calculate the self-energy, Maki-Thompson, and Aslamazov-Larkin diagrams for a dynamically screened Coulomb potential and find that χ''(q, ω) scales as q²ω and the damping rate scales as q². We show that the same result follows from the Einstein relation between the conductivity and charge susceptibility.