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Register a new userEffect of charged line defects on conductivity in graphene: numerical Kubo and analytical Boltzmann approaches
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Charge carrier transport in single-layer graphene with one-dimensional charged defects is studied theoretically. Extended charged defects, considered an important factor for mobility degradation in chemically-vapor-deposited graphene, are described by a self-consistent Thomas-Fermi potential. A numerical study of electronic transport is performed by means of a time-dependent real-space Kubo approach in honeycomb lattices containing millions of carbon atoms, capturing the linear response of realistic size systems in the highly disordered regime. Our numerical calculations are complemented with a kinetic transport theory describing charge transport in the weak scattering limit. The semiclassical transport lifetimes are obtained by computing scattered amplitudes within the second Born approximation. The transport electron-hole asymmetry found in the semiclassical approach is consistent with the Kubo calculations. In the strong scattering regime, the conductivity is found to be a sublinear function of electronic density and weakly dependent on the Thomas-Fermi screening wavelength. We attribute this atypical behavior to the extended nature of one-dimensional charged defects. Our results are consistent with recent experimental reports.
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A Drude-Boltzmann theory is used to calculate the transport properties of bilayer graphene. We find that for typical carrier densities accessible in graphene experiments, the dominant scattering mechanism is overscreened Coulomb impurities that behave like short-range scatterers. We anticipate that the conductivity $sigma(n)$ is linear in $n$ at high density and has a plateau at low density corresponding to a residual density of $n^* = sqrt{n_{rm imp} {tilde n}}$, where ${tilde n}$ is a constant which we estimate using a self-consistent Thomas-Fermi screening approximation to be ${tilde n} approx 0.01 ~q_{rm TF}^2 approx 140 times 10^{10} {rm cm}^{-2}$. Analytic results are derived for the conductivity as a function of the charged impurity density. We also comment on the temperature dependence of the bilayer conductivity.
Theoretical predictions and recent experimental results suggest one can engineer spin Hall effect in graphene by enhancing the spin-orbit coupling in the vicinity of an impurity. We use a Chebyshev expansion of the Kubo-Bastin formula to compute the spin conductivity tensor for a tight-binding model of graphene with randomly distributed impurities absorbed on top of carbon atoms. We model the impurity-induced spin-orbit coupling with a graphene-only Hamiltonian that takes into account three different contributions~cite{Gmitra2013} and show how the spin Hall and longitudinal conductivities depend on the strength of each spin-orbit coupling and the concentration of impurities. Additionally, we calculate the real-space projection of the density of states in the vicinity of the Dirac point for single and multiple impurities and correlate these results with the conductivity calculations.
The effect of Coulomb scattering on graphene conductivity in field effect transistor structures is discussed. Inter-particle scattering (electron-electron, hole-hole, and electron-hole) and scattering on charged defects are taken into account in a wide range of gate voltages. It is shown that an intrinsic conductivity of graphene (purely ambipolar system where both electron and hole densities exactly coincide) is defined by strong electron-hole scattering. It has a universal value independent of temperature. We give an explicit derivation based on scaling theory. When there is even a small discrepancy in electron and hole densities caused by applied gate voltage the conductivity is determined by both strong electron-hole scattering and weak external scattering: on defects or phonons. We suggest that a density of charged defects (occupancy of defects) depends on Fermi energy to explain a sub-linear dependence of conductivity on a fairly high gate voltage observed in experiments. We also eliminate contradictions between experimental data obtained in deposited and suspended graphene structures regarding graphene conductivity.
Exact numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regime. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study (Yan and Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)) and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.
We derive analytical expressions for the conductivity of bilayer graphene (BLG) using the Boltzmann approach within the the Born approximation for a model of Gaussian disorders describing both short- and long-range impurity scattering. The range of validity of the Born approximation is established by comparing the analytical results to exact tight-binding numerical calculations. A comparison of the obtained density dependencies of the conductivity with experimental data shows that the BLG samples investigated experimentally so far are in the quantum scattering regime where the Fermi wavelength exceeds the effective impurity range. In this regime both short- and long-range scattering lead to the same linear density dependence of the conductivity. Our calculations imply that bilayer and single layer graphene have the same scattering mechanisms. We also provide an upper limit for the effective, density dependent spatial extension of the scatterers present in the experiments.
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