Auger recombination in Dirac materials: A tangle of many-body effects

The peculiar electron dispersion in Dirac materials makes lowest-order Auger processes prohibited or marginally prohibited by energy and momentum conservation laws. Thus, Auger recombination (AR) in these materials is very sensitive to many-body effects. We incorporate them at the level of the $GW$ approximation into the nonequilibrium Green's functions approach to AR and study the role of dynamic screening, spectrum broadening and renormalization in the case of weakly pumped undoped graphene. We find that incorrect treatment of many-body effects can lead to an order-of-magnitude error in the recombination rate. We show that the AR time weakly (sublinearly) depends on the background dielectric constant, which limits the possibility to control recombination by the choice of substrate. However, the AR time can be considerably prolonged by placing graphene under a metal gate or by introducing a bandgap. With carrier cooling taken into account, our results comply with experiments on photoexcited graphene.