Theory of shot noise in strange metals

We extend the theory of shot noise in coherent metals to shot noise in strange metals without quasiparticle excitations. This requires a generalization of the Boltzmann equation with a noise source to distribution functions which depend independently on the excitation momentum and energy. We apply this theory to a model of a strange metal with linear in temperature ($T$) resistivity, describing a Fermi surface with a spatially random Yukawa coupling to a critical boson. We find a suppression of the Fano factor in the strange metal, and describe the dependence of the shot noise on temperature and applied voltage. At low temperatures, we obtain a Fano factor equal to $1/6$, in contrast to the $1/3$ Fano factor in diffusive metals with quasiparticles. Our results are in general agreement with recent observations by Chen et al. (arXiv:2206.00673). We further compare the random Yukawa model to quasi-elastic electron-phonon scattering that also generates $T$-linear resistivity, and argue that shot noise observations offer a useful diagnostic to distinguish between them.