Electron-Hole Generation and Recombination Rates for Coulomb Scattering in Graphene

We calculate electron-hole generation and recombination rates for Coulomb scattering (Auger recombination and impact ionization) in Graphene. The conduction and valence band dispersion relation in Graphene together with energy and momentum conservation requirements restrict the phase space for Coulomb scattering so that electron-hole recombination times can be much longer than 1 ps for electron-hole densities smaller than $10^{12}$ cm$^{-2}$.