Abstract
We analyze optical conductivity of a clean two-dimensional electron system in a Fermi liquid regime near a T=0 Ising-nematic quantum critical point (QCP), and extrapolate the results to a QCP. We employ direct perturbation theory up to the two-loop order to elucidate how the Fermi surface's geometry (convex vs. concave) and fermionic dispersion (parabolic vs. non-parabolic) affect the scaling of the optical conductivity, σ(ω), with frequency ω and correlation length ξ. We find that for a convex Fermi surface the leading terms in the optical conductivity cancel out, leaving a sub-leading contribution σ (ω) ∝ ω² ξ⁴ L, where L = const for a parabolic dispersion and L ∝ logω ξ³ in a generic case. For a concave Fermi surface, the leading terms do not cancel, and σ (ω) ∝ ξ². We extrapolate these results to a QCP and obtain σ (ω) ∝ ω^2/3 for a convex Fermi surface and σ (ω) ∝ 1/ω^2/3 for a concave Fermi surface.