Electronic States of Graphene Nanoribbons

We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particle- and a hole-like band with evanescent wavefunctions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units is divisible by 3, and insulating otherwise. A comparison of the wavefunctions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.Comment: 5 pages, 6 figure

Low-thrust chemical propulsion system propellant expulsion and thermal conditioning study. Executive summary

Preferred techniques for providing abort pressurization and engine feed system net positive suction pressure (NPSP) for low thrust chemical propulsion systems (LTPS) were determined. A representative LTPS vehicle configuration is presented. Analysis tasks include: propellant heating analysis; pressurant requirements for abort propellant dump; and comparative analysis of pressurization techniques and thermal subcoolers

Low-thrust chemical propulsion system propellant expulsion and thermal conditioning study

Thermal conditioning systems for satisfying engine net positive suction pressure (NPSP) requirements, and propellant expulsion systems for achieving propellant dump during a return-to-launch site (RTLS) abort were studied for LH2/LO2 and LCH4/LO2 upper stage propellant combinations. A state-of-the-art thermal conditioning system employing helium injection beneath the liquid surface shows the lowest weight penalty for LO2 and LCH4. A technology system incorporating a thermal subcooler (heat exchanger) for engine NPSP results in the lowest weight penalty for the LH2 tank. A preliminary design of two state-of-the-art and two new technology systems indicates a weight penalty difference too small to warrant development of a LH2 thermal subcooler. Analysis results showed that the LH2/LO2 propellant expulsion system is optimized for maximum dump line diameters, whereas the LCH4/LO2 system is optimized for minimum dump line diameter (LCH4) and maximum dump line diameter (LO2). The primary uncertainty is the accurate determination of two-phase flow rates through the dump system; experimentation is not recommended because this uncertainty is not considered significant

Numerical study of the lattice vacancy effects on the single-channel electron transport of graphite ribbons

Lattice vacancy effects on electrical conductance of nanographite ribbon are investigated by means of the Landauer approach using a tight binding model. In the low-energy regime ribbons with zigzag boundary provide a single conducting channel whose origin is connected with the presence of edge states. It is found that the chemical potential dependence of conductance strongly depends on the difference ($\Delta$) of the number of removed A and B sublattice sites. The large lattice vacancy with $\Delta\neq 0$ shows $2\Delta$ zero-conductance dips in the single-channel region, however, the large lattice vacancy with $\Delta=0$ has no dip structure in this region. The connection between this conductance rule and the Longuet-Higgins conjecture is also discussed

Experience with Carbon Taxes and Greenhouse Gas Emissions Trading Systems

Carbon taxes and emissions trading systems (ETSs) to limit emissions of greenhouse gases (GHGs) are increasingly common. At the end of 2015, 17 GHG ETSs were operational in 55 jurisdictions, and 18 jurisdictions collected at least one carbon tax. This paper assesses the performance of carbon taxes and ETSs with respect to environmental effectiveness (reduction of emissions regulated by the instrument), cost-effectiveness (marginal abatement cost), economic efficiency, public finance, and administrative issues. Data on emissions subject to carbon taxes are rarely reported. We estimate the taxed emissions for 17 taxes in 12 jurisdictions from 1991 through the end of 2015. All 17 taxes have reduced emissions relative to business-as-usual. Six of the jurisdictions actually reduced emissions, although in at least three of those jurisdictions the reductions appear to be due to other policies. The small sizes of reduction in almost all 17 cases are partially due to the low tax rates; the modest and uncertain changes in tax rates over time; and the limited response of taxed sources, such as fossil fuels, to price changes. Actual emissions declined for at least six of 10 ETSs. Other policies and developments, such as the 2009 recession, contributed to the reductions, but estimates of the share of the reduction attributable to the instrument are rare. All of the ETSs have accumulated banks of surplus allowances and most have implemented measures to reduce these banks. On average, the marginal cost of compliance is substantially lower for ETSs than carbon taxes. ETS experience has been shared bilaterally and via dedicated institutions. As a result, most ETSs have increased the share of allowances auctioned; adopted declining emissions caps; specified future caps and floor prices several years into the future; shifted to benchmarking for free allowance allocations to emissions-intensive, trade-exposed (EITE) sources; reduced accessibility to foreign offset credits; and established market stability reserves. By contrast, there is little evidence of shared learning and virtually no change to the design of carbon taxes. We found no jurisdiction that routinely tracks the taxed emissions. Very few jurisdictions regularly assess the effectiveness of the tax in achieving emission reductions. Additionally, adjustments to the tax rate often are unpredictable after an introductory period of three to five years. Both instruments reduce emissions, but ETSs have performed better than carbon taxes on the principal criteria of environmental effectiveness and cost-effectiveness. Many jurisdictions have implemented both a carbon tax and a GHG ETS, and every jurisdiction that has adopted either instrument has also implemented other policies. More research is needed to improve the design of both instruments and their interaction with non-market-based carbon policies because the use of multiple instruments produces complex interactive and distributional effects. While economically inefficient, market-based policies should be supplemented by non-market-based policies to ensure sustained political support

The statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the flow of granular material through vertical channels. Our study is confined to dense, slow flows where the material shears like a fluid only in thin layers adjacent to the walls, while a large core moves without continuous deformation, like a solid. We find the velocity distribution to be non-Gaussian, anisotropic, and to follow a power law at large velocities. Remarkably, the distribution is identical in the fluid-like and solid-like regions. The velocity variance is maximum at the core, defying predictions of hydrodynamic theories. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.Comment: Submitted to Phys. Rev. Let

Electronic and Magnetic Properties of Nanographite Ribbons

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in magnetic field, generating a rational fraction of the magnetic flux (\phi= p/q) in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, it is shown that the crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior of the magnetic susceptibility of nanographite ribbons with zigzag edges.Comment: 13 pages including 19 figures, submitted to Physical Rev

Instabilities at [110] Surfaces of d_{x^2-y^2} Superconductors

We compare different scenarios for the low temperature splitting of the zero-energy peak in the local density of states at (110) surfaces of d_{x^2-y^2}-wave superconductors, observed by Covington et al. (Phys.Rev.Lett.79 (1997), 277). Using a tight binding model in the Bogolyubov-de Gennes treatment we find a surface phase transition towards a time-reversal symmetry breaking surface state carrying spontaneous currents and an s+id-wave state. Alternatively, we show that electron correlation leads to a surface phase transition towards a magnetic state corresponding to a local spin density wave state.Comment: 4 pages, 5 figure

Soliton Trap in Strained Graphene Nanoribbons

The wavefunction of a massless fermion consists of two chiralities, left-handed and right-handed, which are eigenstates of the chiral operator. The theory of weak interactions of elementally particle physics is not symmetric about the two chiralities, and such a symmetry breaking theory is referred to as a chiral gauge theory. The chiral gauge theory can be applied to the massless Dirac particles of graphene. In this paper we show within the framework of the chiral gauge theory for graphene that a topological soliton exists near the boundary of a graphene nanoribbon in the presence of a strain. This soliton is a zero-energy state connecting two chiralities and is an elementally excitation transporting a pseudospin. The soliton should be observable by means of a scanning tunneling microscopy experiment.Comment: 7 pages, 4 figure

Correlation effects of carbon nanotubes at boundaries: Spin polarization induced by zero-energy boundary states

When a carbon nanotube is truncated with a certain type of edges, boundary states localized near the edges appear at the fermi level. Starting from lattice models, low energy effective theories are constructed which describe electron correlation effects on the boundary states. We then focus on a thin metallic carbon nanotube which supports one or two boundary states, and discuss physical consequences of the interaction between the boundary states and bulk collective excitations. By the renormalization group analyses together with the open boundary bosonization, we show that the repulsive bulk interactions suppress the charge fluctuations at boundaries, and assist the spin polarization.Comment: 8 pages, 1 figur