924 research outputs found

    Spectral Properties and Linear Stability of Self-Similar Wave Maps

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    We study co--rotational wave maps from (3+1)(3+1)--Minkowski space to the three--sphere S3S^3. It is known that there exists a countable family {fn}\{f_n\} of self--similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well--posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from fnf_n by letting nn \to \infty.Comment: Some extensions added to match the published versio

    Tunable Superconducting Phase Transition in Metal-Decorated Graphene Sheets

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    Using typical experimental techniques it is difficult to separate the effects of carrier density and disorder on the superconducting transition in two dimensions. Using a simple fabrication procedure based on metal layer dewetting, we have produced graphene sheets decorated with a non-percolating network of nanoscale tin clusters. These metal clusters both efficiently dope the graphene substrate and induce long-range superconducting correlations. This allows us to study the superconducting transition at fixed disorder and variable carrier concentration. We find that despite structural inhomogeneity on mesoscopic length scales (10-100 nm), this material behaves electronically as a homogenous dirty superconductor. Our simple self-assembly method establishes graphene as an ideal tunable substrate for studying induced two-dimensional electronic systems at fixed disorder and our technique can readily be extended to other order parameters such as magnetism

    Chemical doping of individual semiconducting carbon-nanotube ropes

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    We report the effects of potassium doping on the conductance of individual semiconducting single-walled carbon nanotube ropes. We are able to control the level of doping by reversibly intercalating and de-intercalating potassium. Potassium doping changes the carriers in the ropes from holes to electrons. Typical values for the carrier density are found to be ∼100–1000 electrons/μm. The effective mobility for the electrons is μeff∼20–60 cm2 V-1 s-1, a value similar to that reported for the hole effective mobility in nanotubes [R. Martel et al., Appl. Phys. Lett. 73, 2447 (1998)]

    Instability of two dimensional graphene: Breaking sp2 bonds with soft X-rays

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    We study the stability of various kinds of graphene samples under soft X-ray irradiation. Our results show that in single layer exfoliated graphene (a closer analogue to two dimensional material), the in-plane carbon-carbon bonds are unstable under X-ray irradiation, resulting in nanocrystalline structures. As the interaction along the third dimension increases by increasing the number of graphene layers or through the interaction with the substrate (epitaxial graphene), the effect of X-ray irradiation decreases and eventually becomes negligible for graphite and epitaxial graphene. Our results demonstrate the importance of the interaction along the third dimension in stabilizing the long range in-plane carbon-carbon bonding, and suggest the possibility of using X-ray to pattern graphene nanostructures in exfoliated graphene.Comment: 4 pages, 3 figures, Phys. Rev. B rapid communication, in pres