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Register a new userConductivity and scattering in graphene bilayers: numerically exact results vs. Boltzmann approach
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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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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.
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.
Different scattering mechanisms in graphene are explored and conductivity is calculated within the Boltzmann transport theory. We provide results for short-range scattering using the Random Phase Approximation for electron screening, as well as analytical expressions for the dependence of conductivity on the dielectric constant of the substrate. We further examine the effect of ripples on the transport using a surface roughness model developed for semiconductor heterostructures. We find that close to the Dirac point, sigma sim n^beta, where beta=1,0,-2 for Coulomb, short-range and surface roughness respectively; implying that Coulomb scattering dominates over both short-range and surface roughness scattering at low density.
The conductivity of graphene samples with various levels of disorder is investigated for a set of specimens with mobility in the range of $1-20times10^3$ cm$^2$/V sec. Comparing the experimental data with the theoretical transport calculations based on charged impurity scattering, we estimate that the impurity concentration in the samples varies from $2-15times 10^{11}$ cm$^{-2}$. In the low carrier density limit, the conductivity exhibits values in the range of $2-12e^2/h$, which can be related to the residual density induced by the inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain some short range disorder whereas low mobility samples are dominated by long range scatterers.
We theoretically examine the effect of carrier-carrier scattering processes (electron-hole and electron-electron) on the intraband radiation absorption and their contribution to the net dynamic conductivity in optically or electrically pumped graphene. We demonstrate that the radiation absorption assisted by the carrier-carrier scattering can be stronger than the Drude absorption due to the carrier scattering on disorder. Since the intraband absorption of radiation effectively competes with its interband amplification, this can substantially affect the conditions of the negative dynamic conductivity in the pumped graphene and, hence, the interband terahertz and infrared lasing. We find the threshold values of the frequency and quasi-Fermi energy of nonequilibrium carriers corresponding to the onset of negative dynamic conductivity. The obtained results show that the effect of carrier-carrier scattering shifts the threshold frequency of the radiation amplification in pumped graphene to higher values. In particular, the negative dynamic conductivity is attainable at the frequencies above 6 THz in graphene on SiO2 substrates at room temperature. The threshold frequency can be decreased to markedly lower values in graphene structures with high-k substrates due to screening of the carrier-carrier scattering, particularly at lower temperatures.
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