Curvature, hybridization, and STM images of carbon nanotubes

The curvature effects in carbon nanotubes are studied analytically as a function of chirality. The pi-orbitals are found to be significantly rehybridized in all tubes, so that they are never normal to the tubes' surface. This results in a curvature induced gap in the electronic band-structure, which turns out to be larger than previous estimates. The tilting of the pi-orbitals should be observable by atomic resolution scanning tunneling microscopy measurements.Comment: Four pages in revtex format including four epsfig-embedded figures. The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/hybrid.pd

Size, Shape and Low Energy Electronic Structure of Carbon Nanotubes

A theory of the long wavelength low energy electronic structure of graphite-derived nanotubules is presented. The propagating $\pi$ electrons are described by wrapping a massless two dimensional Dirac Hamiltonian onto a curved surface. The effects of the tubule size, shape and symmetry are included through an effective vector potential which we derive for this model. The rich gap structure for all straight single wall cylindrical tubes is obtained analytically in this theory, and the effects of inhomogeneous shape deformations on nominally metallic armchair tubes are analyzed.Comment: 5 pages, 3 postscript figure

Supporting Situation Awareness and Decision Making in Weather Forecasting

Weather forecasting is full of uncertainty, and as in domains such as air traffic control or medical decision making, decision support systems can affect a forecaster’s ability to make accurate and timely judgments. Well-designed decision aids can help forecasters build situation awareness (SA), a construct regarded as a component of decision making. SA involves the ability to perceive elements within a system, comprehend their significance, and project their meaning into the future in order to make a decision. However, how SA is affected by uncertainty within a system has received little attention. This tension between managing uncertainty, situation assessment, and the impact that technology has on the two, is the focus of this dissertation. To address this tension, this dissertation is centered on the evaluation of a set of coupled models that integrate rainfall observations and hydrologic simulations, coined “the FLASH system” (Flooded Locations and Simulated Hydrographs project). Prediction of flash flooding is unique from forecasting other weather-related threats due to its multi-disciplinary nature. In the United States, some weather forecasters have limited hydrologic forecasting experience. Unlike FLASH, current flash flood forecasting tools are based upon rainfall rates, and with the recent expansion into coupled rainfall and hydrologic models, forecasters have to learn quickly how to incorporate these new data sources into their work. New models may help forecasters to increase their prediction skill, but no matter how far the technology advances, forecasters must be able to accept and integrate the new tools into their work in order to gain any benefit. A focus on human factors principles in the design stage can help to ensure that by the time the product is transitioned into operational use, the decision support system addresses users’ needs while minimizing task time, workload, and attention constraints. This dissertation discusses three qualitative and quantitative studies designed to explore the relationship between flash flood forecasting, decision aid design, and SA. The first study assessed the effects of visual data aggregation methods on perception and comprehension of a flash flood threat. Next, a mixed methods approach described how forecasters acquire SA and mitigate situational uncertainty during real-time forecasting operations. Lastly, the third study used eye tracking assessment to identify the effects of an automated forecasting decision support tool on SA and information scanning behavior. Findings revealed that uncertainty management in forecasting involves individual, team, and organizational processes. We make several recommendations for future decision support systems to promote SA and performance in the weather forecasting domain

Electronic Structure of Carbon Nanotube Ropes

We present a tight binding theory to analyze the motion of electrons between carbon nanotubes bundled into a carbon nanotube rope. The theory is developed starting from a description of the propagating Bloch waves on ideal tubes, and the effects of intertube motion are treated perturbatively in this basis. Expressions for the interwall tunneling amplitudes between states on neighboring tubes are derived which show the dependence on chiral angles and intratube crystal momenta. We find that conservation of crystal momentum along the tube direction suppresses interwall coherence in a carbon nanorope containing tubes with random chiralities. Numerical calculations are presented which indicate that electronic states in a rope are localized in the transverse direction with a coherence length corresponding to a tube diameter.Comment: 15 pages, 10 eps figure

Electric Polarization of Heteropolar Nanotubes as a Geometric Phase

The three-fold symmetry of planar boron nitride, the III-V analog to graphene, prohibits an electric polarization in its ground state, but this symmetry is broken when the sheet is wrapped to form a BN nanotube. We show that this leads to an electric polarization along the nanotube axis which is controlled by the quantum mechanical boundary conditions on its electronic states around the tube circumference. Thus the macroscopic dipole moment has an {\it intrinsically nonlocal quantum} mechanical origin from the wrapped dimension. We formulate this novel phenomenon using the Berry's phase approach and discuss its experimental consequences.Comment: 4 pages with 3 eps figures, updated with correction to Eqn (9

The Electronic Spectrum of Fullerenes from the Dirac Equation

The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found that a Dirac equation describes the flat graphite lattice. Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center.Comment: 29 pages, 7 figures. IASSNS-HEP-92/5

Electronic structure, vibrational stability, infra-red, and Raman spectra of B24N24 cages

We examine the vibrational stability of three candidate structures for the B24N24 cage and report their infra-red (IR) and Raman spectra. The candidate structures considered are a round cage with octahedral O symmetry, a cage with S_4 symmetry that satisfies the isolated square rule, and a cage of S_8 symmetry, which combines the caps of the (4,4) nanotube, and contains two extra squares and octagons. The calculations are performed within density functional theory, at the all electron level, with large basis sets, and within the generalized gradient approximation. The vertical ionization potential (VIP) and static dipole polarizability are also reported. The S_4 and S_8 cages are energetically nearly degenerate and are favored over the O cage which has six extra octagons and squares. The IR and Raman spectra of the three clusters show notable differences providing thereby a way to identify and possibly synthesize the cages.Comment: (Uses Elsevier style file; To appear in Chemical Physics Letters

Fermi level quantum numbers and secondary gap of conducting carbon nanotubes

For the single-wall carbon nanotubes conducting in the simplest tight binding model, the complete set of line group symmetry based quantum numbers for the bands crossing at Fermi level are given. Besides linear (k), helical (k'} and angular momenta, emerging from roto-translational symmetries, the parities of U axis and (in the zig-zag and armchair cases only) mirror planes appear in the assignation. The helical and angular momentum quantum numbers of the crossing bands never vanishes, what supports proposed chirality of currents. Except for the armchair tubes, the crossing bands have the same quantum numbers and, according to the non-crossing rule, a secondary gap arises, as it is shown by the accurate tight-binding calculation. In the armchair case the different vertical mirror parity of the crossing bands provides substantial conductivity, though kF is slightly decreased.Comment: 6 pages, 2 figure

Superconducting and charge-density wave instabilities in ultrasmall-radius carbon nanotubes

We perform a detailed analysis of the band structure, phonon dispersion, and electron-phonon coupling of three types of small-radius carbon nanotubes (CNTs): (5,0), (6,0), and (5,5) with diameters 3.9, 4.7, and 6.8 \AA respectively. The large curvature of the (5,0) CNTs makes them metallic with a large density of states at the Fermi energy. The density of states is also strongly enhanced for the (6,0) CNTs compared to the results obtained from the zone-folding method. For the (5,5) CNTs the electron-phonon interaction is dominated by the in-plane optical phonons, while for the ultrasmall (5,0) and (6,0) CNTs the main coupling is to the out-of-plane optical phonon modes. We calculate electron-phonon interaction strengths for all three types of CNTs and analyze possible instabilities toward superconducting and charge-density wave phases. For the smallest (5,0) nanotube, in the mean-field approximation and neglecting Coulomb interactions, we find that the charge-density wave transition temperature greatly exceeds the superconducting one. When we include a realistic model of the Coulomb interaction we find that the charge-density wave is suppressed to very low temperatures, making superconductivity dominant with the mean-field transition temperature around one K. For the (6,0) nanotube the charge-density wave dominates even with the inclusion of Coulomb interactions and we find the mean-field transition temperature to be around five Kelvin. We find that the larger radius (5,5) nanotube is stable against superconducting and charge-density wave orders at all realistic temperatures.Comment: 5 pages. 2 figure

Dimerization structures on the metallic and semiconducting fullerene tubules with half-filled electrons

Possible dimerization patterns and electronic structures in fullerene tubules as the one-dimensional pi-conjugated systems are studied with the extended Su-Schrieffer-Heeger model. We assume various lattice geometries, including helical and nonhelical tubules. The model is solved for the half-filling case of $\pi$-electrons. (1) When the undimerized systems do not have a gap, the Kekule structures prone to occur. The energy gap is of the order of the room temperatures at most and metallic properties would be expected. (2) If the undimerized systems have a large gap (about 1eV), the most stable structures are the chain-like distortions where the direction of the arranged trans-polyacetylene chains is along almost the tubular axis. The electronic structures are ofsemiconductors due to the large gap.Comment: submitted to Phys. Rev. B, pages 15, figures 1