Graphene made easy: high quality, large-area samples

We show that by using an original method, bulk graphite can be bonded onto borosilicate glass or potentially any insulating substrate with ionic conductivity and then cleaved off to leave single or few layer graphene on the substrate, identified optically and with Raman spectroscopy. This simple, inexpensive and fast method leads to the preparation of large area graphene and single or few-layer films of layered materials in general. We have prepared mm size few-layer graphene samples and also measured I-V characteristics in a FET. This opens up perspectives both for fundamental research as well as for applications.Comment: 11 pages, 4 figures,Solid State Communications, In pres

The Significant Digit Law in Statistical Physics

The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford's law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann-Gibbs (BG) distribution, the Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around the Benford distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus the Benford's law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford's law, especially the mantissa distribution of data sets, are discussed.Comment: 21 latex pages, 5 figures, final version in journal publicatio

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao

CO2 Laser-Induced Growth of Epitaxial Graphene on 6H-SiC(0001)

The thermal decomposition of SiC surface provides, perhaps, the most promising method for the epitaxial growth of graphene on a material useful in the electronics platform. Currently, efforts are focused on a reliable method for the growth of large-area, low-strain epitaxial graphene that is still lacking. We report here a novel method for the fast, single-step epitaxial growth of large-area homogeneous graphene film on the surface of SiC(0001) using an infrared CO2 laser (10.6 {\mu}m) as the heating source. Apart from enabling extreme heating and cooling rates, which can control the stacking order of epitaxial graphene, this method is cost-effective in that it does not necessitate SiC pre-treatment and/or high vacuum, it operates at low temperature and proceeds in the second time scale, thus providing a green solution to EG fabrication and a means to engineering graphene patterns on SiC by focused laser beams. Uniform, low-strain graphene film is demonstrated by scanning electron microscopy and x-ray photoelectron, secondary ion mass, and Raman spectroscopies. Scalability to industrial level of the method described here appears to be realistic, in view of the high rate of CO2-laser induced graphene growth and the lack of strict sample-environment conditions.Comment: 32 pages, 5 figures, includes Supporting Informatio

Raman Topography and Strain Uniformity of Large-Area Epitaxial Graphene

We report results from two-dimensional Raman spectroscopy studies of large-area epitaxial graphene grown on SiC. Our work reveals unexpectedly large variation in Raman peak position across the sample resulting from inhomogeneity in the strain of the graphene film, which we show to be correlated with physical topography by coupling Raman spectroscopy with atomic force microscopy. We report that essentially strain free graphene is possible even for epitaxial graphene.Comment: 10 pages, 3 figure

Surface energy engineering of graphene

Contact angle goniometry is conducted for epitaxial graphene on SiC. Although only a single layer of epitaxial graphene exists on SiC, the contact angle drastically changes from 69{\deg} on SiC substrates to 92{\deg} with graphene. It is found that there is no thickness dependence of the contact angle from the measurements of single, bi, and multi layer graphene and highly ordered pyrolytic graphite (HOPG). After graphene is treated with oxygen plasma, the level of damage is investigated by Raman spectroscopy and correlation between the level of disorder and wettability is reported. By using low power oxygen plasma treatment, the wettability of graphene is improved without additional damage, which can solve the adhesion issues involved in the fabrication of graphene devices

Differential Conductance Fluctuation of Curved Nanographite Sheets in the Mesoscopic Regime

Excess conductance fluctuations with peculiar temperature-dependence from 1.4 to 250 K were observed in curved nano-graphite sheets with an electrode gap length of 300 and 450 nm, whereas the conductance fluctuation is greatly suppressed above 4.2 K when the electrode gap length increases to 800 and 1000 nm. The former is discussed in the context of the presence of a small energy bandgap in the nano-graphite sheets, while the latter is attributed to the crossover from coherent transport to diffusive transport regime.Comment: 12 pages, 3 figure

Regularization of point vortices for the Euler equation in dimension two

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem [ -\ep^2 \Delta u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, ] where $p>1$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function. We showed that if $\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function $\mathcal{W}(x_1,...,x_m)$ with the same strength $\kappa>0$, there is a stationary classical solution approximating stationary $m$ points vortex solution of incompressible Euler equations with vorticity $m\kappa$. Existence and asymptotic behavior of single point non-vanishing vortex solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page

Chandrasekhar-Kendall functions in astrophysical dynamos

Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number.Comment: 10 pages, 5 figures, proceedings of the Chandrasekhar Centenary Conference, to be published in PRAMANA - Journal of Physic

Probing the close environment of young stellar objects with interferometry

The study of Young Stellar Objects (YSOs) is one of the most exciting topics that can be undertaken by long baseline optical interferometry. The magnitudes of these objects are at the edge of capabilities of current optical interferometers, limiting the studies to a few dozen, but are well within the capability of coming large aperture interferometers like the VLT Interferometer, the Keck Interferometer, the Large Binocular Telescope or 'OHANA. The milli-arcsecond spatial resolution reached by interferometry probes the very close environment of young stars, down to a tenth of an astronomical unit. In this paper, I review the different aspects of star formation that can be tackled by interferometry: circumstellar disks, multiplicity, jets. I present recent observations performed with operational infrared interferometers, IOTA, PTI and ISI, and I show why in the next future one will extend these studies with large aperture interferometers.Comment: Review to be published in JENAM'2002 proceedings "The Very Large Telescope Interferometer Challenges for the future