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We consider two-dimensional metals near a Pomeranchuk instability whichbreaks 90$^\circ$ lattice rotation symmetry. Such metals realizestrongly-coupled non-Fermi liquids with critical fluctuations of anIsing-nematic order. At low temperatures, impurity scattering provides thedominant source of momentum relaxation, and hence a non-zero electricalresistivity. We use the memory matrix method to compute the resistivity of thisnon-Fermi liquid to second order in the impurity potential, without assumingthe existence of quasiparticles. Impurity scattering in the $d$-wave channelacts as a random "field" on the Ising-nematic order. We find contributions tothe resistivity with a nearly linear temperature dependence, along with moresingular terms; the most singular is the random-field contribution whichdiverges in the limit of zero temperature.

Transport near the Ising-nematic quantum critical point of metals in two dimensions