Single particle relaxation time versus transport scattering time in a 2D graphene layer

We theoretically calculate and compare the single-particle relaxation time ($\tau_s$) defining quantum level broadening and the transport scattering time ($\tau_t$) defining Drude conductivity in 2D graphene layers in the presence of screened charged impurities scattering and short-range defect scattering. We find that the ratio $\tau_t/\tau_s$ increases strongly with increasing $k_F z_i$ and $\kappa$ where $k_F$, $z_i$, and $\kappa$ are respectively the Fermi wave vector, the separation of the substrate charged impurities from the graphene layer, and the background lattice dielectric constant. A critical quantitative comparison of the $\tau_t/\tau_s$ results for graphene with the corresponding modulation-doped semiconductor structures is provided, showing significant differences between these two 2D carrier systems.