  Graphene is an ideal material to study fundamental Coulomb- and
phonon-induced carrier scattering processes. Its remarkable gapless and linear
band structure opens up new carrier relaxation channels. In particular, Auger
scattering bridging the valence and the conduction band changes the number of
charge carriers and gives rise to a significant carrier multiplication - an
ultrafast many-particle phenomenon that is promising for the design of highly
efficient photodetectors. Furthermore, the vanishing density of states at the
Dirac point combined with ultrafast phonon-induced intraband scattering results
in an accumulation of carriers and a population inversion suggesting the design
of graphene-based terahertz lasers. Here, we review our work on the ultrafast
carrier dynamics in graphene and Landau-quantized graphene is presented
providing a microscopic view on the appearance of carrier multiplication and
population inversion.
