Shot noise in graphene with long-range Coulomb interaction and local Fermi distribution

We calculate the shot-noise power in ballistic graphene using the kinetic equation approach based on the Keldysh technique. We find that the local energy distribution function obeys Poisson's equation, indicating a mapping into a diffusive metal system. We derive the conductance and noise including the long-range Coulomb interaction to first order. We find that the shot noise increases due to interaction, leading to a frequency dependence. Furthermore, we find that the Fano factor at degeneracy is 1/3, the same as without the Coulomb interaction.