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.
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