Abstract

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., graphene and the surface state of a three-dimensional topological insulator. We study the effect of electron-electron interactions on the optical conductivity of a DFL. It is shown that the effective current relaxation rate behaves as 1/τ_J∼(3ω^4+ 20π^2ω^2T^2+ 32π^4T^4)/μ^3 for max{ω,T}<<μ, where μ is the chemical potential. The quartic term in 1/τ_J competes with a small FL-like term, (ω^2+ 4π^2T^2)/μ, due to weak trigonal warping of graphene dispersion. In the presence of weak disorder, the optical conductivity is described by the sum of two Drude-like terms, with widths given by the electron-electron and electron-impurity scattering rates, respectively. The dc resistivity varies non-monotonically with temperature, approaching the identical values given by the residual resistivity in the limits of both low and high T, with a maximum in between. We also calculated the dynamic charge susceptibility, χ_c(q,ω), outside the particle-hole continua and to one-loop order in the dynamically screened Coulomb interaction. For a DFL, the dissipative part of χ_c(q,ω) scales as q^2ω and is larger than the corresponding quantity for a Galilean-invariant FL, which scales as q^4/ω.