Shot noise in a phenomenological model of a marginal Fermi liquid

The strange metal is a mysterious non-Fermi liquid which shows linear-in-$T$ resistivity behavior at finite temperatures, and, as found in recent experiment, vanishingly small shot noise in the linear-in-$T$ regime. Here, we investigate the shot noise of a strange metal based on a phenomenological model of marginal Fermi liquid (MFL), where fermions couple to some collective boson mode, leading to $T$-linear scattering rate at finite $T$. It is found that in the diffusive regime where the MFL scattering length is small compared to the system size, the shot noise vanishes, and the thermal noise becomes a temperature- and voltage-independent constant. Introducing additional impurity scattering increases the shot noise, and is probably consistent with the current experiment.