Strong non-linear response of strange metals

We show that nonlinear transport responses in strange metals are strong, larger by a factor of $E_F\mathrm{/}T$ than in Fermi liquids. Within the two-dimensional Yukawa-Sachdev-Ye-Kitaev model of a Fermi surface with a spatially random coupling to a critical scalar, the third order conductivity is found to diverge as $1\mathrm{/}T$ at low $T$, indicating the existence of a voltage-temperature scaling regime in the conductance. Its frequency and orientation dependence contains information on relaxation times of heat and electron distribution deformations, providing a new set of tools to characterize strange metals.