  The nonequilibrium dynamics of carriers and phonons in graphene is
investigated by solving the microscopic kinetic equations with the
carrier-phonon and carrier-carrier Coulomb scatterings explicitly included. The
Fermi distribution of hot carriers are found to be established within 100 fs
and the temperatures of electrons in the conduction and valence bands are very
close to each other, even when the excitation density and the equilibrium
density are comparable, thanks to the strong inter-band Coulomb scattering.
Moreover, the temporal evolutions of the differential transmission obtained
from our calculations agree with the experiments by Wang et al. [Appl. Phys.
Lett. 96, 081917 (2010)] and Hale et al. [Phys. Rev. B 83, 121404 (2011)] very
well, with two distinct differential transmission relaxations presented. We
show that the fast relaxation is due to the rapid carrier-phonon thermalization
and the slow one is mainly because of the slow decay of hot phonons. In
addition, it is found that the temperatures of the hot phonons in different
branches are different and the temperature of hot carriers can be even lower
than that of the hottest phonons. Finally, we show that the slow relaxation
rate exhibits a mild valley in the excitation density dependence and is
linearly dependent on the probe-photon energy.
