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Register a new userCharged Impurity Scattering in Graphene
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Since the experimental realization of graphene1, extensive theoretical work has focused on short-range disorder2-5, ripples6, 7, or charged impurities2, 3, 8-13 to explain the conductivity as a function of carrier density sigma_(n)[1,14-18], and its minimum value sigma_min near twice the conductance quantum 4e2/h[14, 15, 19, 20]. Here we vary the density of charged impurities nimp on clean graphene21 by deposition of potassium in ultra high vacuum. At non-zero carrier density, charged impurity scattering produces the ubiquitously observed1, 14-18 linear sigma_(n) with the theoretically-predicted magnitude. The predicted asymmetry11 for attractive vs. repulsive scattering of Dirac fermions is observed. Sigma_min occurs not at the carrier density which neutralizes nimp, but rather the carrier density at which the average impurity potential is zero10. Sigma_min decreases initially with nimp, reaching a minimum near 4e2/h at non-zero nimp, indicating that Sigma_min in present experimental samples does not probe Dirac-point physics14, 15, 19, 20 but rather carrier density inhomogeneity due to the impurity potential3, 9, 10.
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We have examined the impact of charged impurity scattering on charge carrier transport in bilayer graphene (BLG) by deposition of potassium in ultra-high vacuum at low temperature. Charged impurity scattering gives a conductivity which is supra-linear in carrier density, with a magnitude similar to single-layer graphene for the measured range of carrier densities of 2-4 x 10^12 cm^-2. Upon addition of charged impurities of concentration n_imp, the minimum conductivity Sigma_min decreases proportional to n_imp^-1/2, while the electron and hole puddle carrier density increases proportional to n_imp^1/2. These results for the intentional deposition of potassium on BLG are in good agreement with theoretical predictions for charged impurity scattering. However, our results also suggest that charged impurity scattering alone cannot explain the observed transport properties of pristine BLG on SiO2 before potassium doping.
We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile as well as graphenes transport properties. We discuss the screening of a single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphenes transport properties due to scattering off charged impurities both at low and high carrier density.
We theoretically calculate the impurity-scattering induced resistivity of twisted bilayer graphene at low twist angles where the graphene Fermi velocity is strongly suppressed. We consider, as a function of carrier density, twist angle, and temperature, both long-ranged Coulomb scattering and short-ranged defect scattering within a Boltzmann theory relaxation time approach. For experimentally relevant disorder, impurity scattering contributes a resistivity comparable to (much larger than) the phonon scattering contribution at high (low) temperatures. Decreasing twist angle leads to larger resistivity, and in general, the resistivity increases (decreases) with increasing temperature (carrier density). Inclusion of the van Hove singularity in the theory leads to a strong increase in the resistivity at higher densities, where the chemical potential is close to a van Hove singularity, leading to an apparent density-dependent plateau type structure in the resistivity, which has been observed in recent transport experiments. We also show that the Matthissens rule is strongly violated in twisted bilayer graphene at low twist angles.
The transport properties of carriers in semiconducting graphene nanoribbons are studied by comparing the effects of phonon, impurity, and line-edge roughness scattering. It is found that scattering from impurities located at the surface of nanoribbons, and from acoustic phonons are as important as line edge roughness scattering. The relative importance of these scattering mechanisms varies with the temperature, Fermi level location, and the width of the ribbons. Based on the analysis, strategies for improvement of low-field mobility are described.
The conductivity of armchair graphene nanoribbons in the presence of short-range impurities and edge roughness is studied theoretically using the Boltzmann transport equation for quasi-one-dimensional systems. As the number of occupied subbands increases, the conductivity due to short-range impurities converges towards the two-dimensional case. Calculations of the magnetoconductivity confirm the edge-roughness-induced dips at cyclotron radii close to the ribbon width suggested by the recent quantum simulations.
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