  We present a numerical study on the intraband optical conductivity of hot
carriers at quasi-equilibria in photoexcited graphene based on the
semiclassical Boltzmann transport equations (BTE) with the aim of understanding
the effects of intrinsic optical phonon and extrinsic coulomb scattering caused
by charged impurities at the graphene--substrate interface. Instead of using
full-BTE solutions, we employ iterative solutions of the BTE and the
comprehensive model for the temporal evolutions of hot-carrier temperature and
hot-optical-phonon occupations to reduce computational costs. Undoped graphene
exhibits large positive photoconductivity owing to the increase in thermally
excited carriers and the reduction in charged impurity scattering. The
frequency dependencies of the photoconductivity in undoped graphene having high
concentrations of charged impurities significantly deviate from those observed
in the simple Drude model, which can be attributed to temporally varying
charged impurity scattering during terahertz (THz) probing in the hot-carrier
cooling process. Heavily doped graphene exhibits small negative
photoconductivity similar to that of the Drude model. In this case, charged
impurity scattering is substantially suppressed by the carrier-screening
effect, and the temperature dependencies of the Drude weight and optical phonon
scattering governs the negative photoconductivity. In lightly doped graphene,
the appearance of negative and positive photoconductivity depends on the
frequency and the crossover from negative photoconductivity to positive emerges
from increasing the charged impurity concentration. This indicates the change
of the dominant scattering mechanism from optical phonons to charged
impurities. Our approach provides a quantitative understanding of non-Drude
behaviors and the temporal evolution of photoconductivity in graphene.
