Single-particle relaxation time versus transport scattering time in a two-dimensional graphene layer

We theoretically calculate and compare the single particle relaxation time $({\ensuremath{\tau}}_{s})$ defining the quantum level broadening and the transport scattering time $({\ensuremath{\tau}}_{t})$ defining the Drude conductivity in two-dimensional (2D) graphene layers in the presence of screened charged impurity scattering and short-range defect scattering. We find that the ratio ${\ensuremath{\tau}}_{t}∕{\ensuremath{\tau}}_{s}$ strongly increases with increasing ${k}_{F}{z}_{i}$ and $\ensuremath{\kappa}$, where ${k}_{F}$, ${z}_{i}$, and $\ensuremath{\kappa}$ 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 ${\ensuremath{\tau}}_{t}∕{\ensuremath{\tau}}_{s}$ results for graphene with those for the corresponding modulation-doped semiconductor structures is provided, showing significant differences between these two 2D carrier systems.