Optical conductivity of Dirac Fermi liquid

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 (ee) interactions on the optical conductivity of a DFL. We find that the effective current relaxation rate behaves as 1/τ_J∼( 3ω⁴+20π²T²ω²+32 π⁴T⁴)/μ³ 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, (ω²+4π²T²)/ 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 ee and electron-impurity scattering rates, respectively. The dc resistivity varies non-monotonically with T, 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 p-h continua to one-loop order in the dynamically screened Coulomb interaction. For a DFL, the dissipative part of χ_c(q,ω) scales as q²ω and is larger than the q⁴/ω scaling for a Galilean-invariant FL.