Electron Interference Effects on the Conductance of Doped Carbon Nanotubes

We investigate the effects of impurity scattering on the conductance of metallic carbon nanotubes as a function of the relative separation of the impurities. First we compute the conductance of a clean (6,6) tube, and the effect of model gold contacts on this conductance. Then, we compute the effect of introducing a single, two, and three oxygen atom impurities. We find that the conductance of a single-oxygen-doped (6,6) nanotube decreases by about 30 % with respect to that of the perfect nanotube. The presence of a second doping atom induces strong changes of the conductance which, however, depend very strongly on the relative position of the two oxygen atoms. We observe regular oscillations of the conductance that repeat over an O-O distance that corresponds to an integral number of half Fermi-wavelengths ($m\lambda_F/2$). These fluctuations reflect strong electron interference phenomena produced by electron scattering from the oxygen defects whose contribution to the resistance of the tube cannot be obtained by simply summing up their individual contributions.Comment: 13 pages, 5 figures (eps and gif), to appear in J.Phys.Che

Exciton Ionization, Franz-Keldysh and Stark Effects in Carbon Nanotubes

We calculate the optical properties of carbon nanotubes in an external static electric field directed along the tube axis. We predict strong Franz-Keldysh oscillations in the first and second band-to-band absorption peaks, quadratic Stark effect of the first two excitons, and the field dependence of the bound exciton ionization rate for a wide range of tube chiralities. We find that the phonon assisted mechanism dominates the dissociation rate in electro-optical devices due to the hot optical phonons. We predict a quadratic dependence of the Sommerfeld factor on the electric field and its increase up to 2000% at the critical field of the full exciton dissociation.Comment: 12 pages, 5 figures, Nano Letters (2007

Probabilistic Reduced-Order Modeling for Stochastic Partial Differential Equations

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of very large systems of algebraic equations. We establish a physically inspired, data-driven coarse-grained model which learns a low- dimensional set of microstructural features that are predictive of the fine-grained model (FG) response. Once learned, those features provide a sharp distribution over the coarse scale effec- tive coefficients of the PDE that are most suitable for prediction of the fine scale model output. This ultimately allows to replace the computationally expensive FG by a generative proba- bilistic model based on evaluating the much cheaper CG several times. Sparsity enforcing pri- ors further increase predictive efficiency and reveal microstructural features that are important in predicting the FG response. Moreover, the model yields probabilistic rather than single-point predictions, which enables the quantification of the unavoidable epistemic uncertainty that is present due to the information loss that occurs during the coarse-graining process

Mobility in semiconducting carbon nanotubes at finite carrier density

Carbon nanotube field-effect transistors operate over a wide range of electron or hole density, controlled by the gate voltage. Here we calculate the mobility in semiconducting nanotubes as a function of carrier density and electric field, for different tube diameters and temperature. The low-field mobility is a non-monotonic function of carrier density, and varies by as much as a factor of 4 at room temperature. At low density, with increasing field the drift velocity reaches a maximum and then exhibits negative differential mobility, due to the non-parabolicity of the bandstructure. At a critical density $\rho_c\sim$ 0.35-0.5 electrons/nm, the drift velocity saturates at around one third of the Fermi velocity. Above $\rho_c$, the velocity increases with field strength with no apparent saturation.Comment: 5 pages, 4 figure

Relaxation of Optically Excited Carriers in Graphene

We explore the relaxation of photo-excited graphene by solving a transient Boltzmann transport equation with electron-phonon (e-ph) and electron-electron (e-e) scattering. Simulations show that when the excited carriers are relaxed by e-ph scattering only, a population inversion can be achieved at energies determined by the photon energy. However, e-e scattering quickly thermalizes the carrier energy distributions washing out the negative optical conductivity peaks. The relaxation rates and carrier multiplication effects are presented as a function of photon energy and dielectric constant.Comment: 4 pages, 4 figure

Radiative Lifetime of Excitons in Carbon Nanotubes

We calculate the radiative lifetime and energy bandstructure of excitons in semiconducting carbon nanotubes, within a tight-binding approach. In the limit of rapid interband thermalization, the radiative decay rate is maximized at intermediate temperatures, decreasing at low temperature because the lowest-energy excitons are optically forbidden. The intrinsic phonons cannot scatter excitons between optically active and forbidden bands, so sample-dependent extrinsic effects that break the symmetries can play a central role. We calculate the diameter-dependent energy splittings between singlet and triplet excitons of different symmetries, and the resulting dependence of radiative lifetime on temperature and tube diameter.Comment: 4 pages, 3 figure