Suppression of shot noise in a dirty marginal Fermi liquid

We study shot noise in a two-dimensional, disordered marginal Fermi liquid (MFL) driven out of equilibrium. We consider electrons with Planckian dissipation on the Fermi surface coupled to quantum-critical bosons in the presence of disorder. In the noninteracting and strong electron-boson drag limits, MFL effects disappear and our theory reproduces known results. For the case where the bosons remain in equilibrium, inelastic scattering strongly suppresses the noise by dissipating the injected energy. Interestingly, we find that MFL effects do play a role in this regime, and give a weak enhancement on top of the otherwise strong suppression. Our results suggest that shot noise can be strongly suppressed in quantum-critical systems, and this scenario may be relevant to recent measurements in a heavy-fermion strange metal.