Electronic screening and correlated superconductivity in carbon nanotubes

A theoretical analysis of the superconductivity observed recently in Carbon nanotubes is proposed. We argue that ultra-small (diameter $\sim 0.4 nm$) single wall carbon nanotubes (with transition temperature $T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$) can superconduct by an electronic mechanism, basically the same in both cases. By a Luttinger liquid -like approach, one finds enhanced superconducting correlations due to the strong screening of the long-range part of the Coulomb repulsion. Based on this finding, we perform a detailed analysis on the resulting Hubbard-like model, and calculate transition temperatures of the same order of magnitude as the measured ones.Comment: 6 pages, 1 figure, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in Phys. Rev.

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in \cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.Comment: under revision in Physical Review

Refraction of a Gaussian Seaway

Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over wavelength and incoming wave propagation direction. Thus, the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply following refraction by random currents. Proper handling of the non-uniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which considered the effect of currents on a plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The crest height or wave height distribution depends primarily on the ``freak index", gamma, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.Comment: 18 pages, 10 figure

Suppression of electron-electron repulsion and superconductivity in Ultra Small Carbon Nanotubes

Recently, ultra-small-diameter Single Wall Nano Tubes with diameter of $\sim 0.4 nm$ have been produced and many unusual properties were observed, such as superconductivity, leading to a transition temperature $T_c\sim 15^oK$, much larger than that observed in the bundles of larger diameter tubes. By a comparison between two different approaches, we discuss the issue whether a superconducting behavior in these carbon nanotubes can arise by a purely electronic mechanism. The first approach is based on the Luttinger Model while the second one, which emphasizes the role of the lattice and short range interaction, is developed starting from the Hubbard Hamiltonian. By using the latter model we predict a transition temperature of the same order of magnitude as the measured one.Comment: 7 pages, 3 figures, to appear in J. Phys.-Cond. Ma

Triggering rogue waves in opposing currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity, $U_0$, and the wave group velocity, $c_g$. We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing Nonlinear Schrodinger equation with non constant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.Comment: 5 pages, 5 figure

Modulation of Luttinger liquid exponents in multiwalled carbon nanotubes

8 págs.; 7 figs. ; PACS number s : 73.63.Fg, 73.22. f, 73.23. bWe develop in this paper a theoretical framework that applies to the intermediate regime between the Coulomb blockade and the Luttinger liquid behavior in multiwalled carbon nanotubes. Our main goal is to confront the experimental observations of transport properties, under conditions in which the thermal energy is comparable to the spacing between the single-particle levels. For this purpose we have devised a many-body approach to the one-dimensional electron system, incorporating the effects of a discrete spectrum. We show that, in the crossover regime, the tunneling conductance follows a power-law behavior as a function of the temperature, with an exponent that oscillates with the gate voltage as observed in the experiments. Also in agreement with the experimental observations, a distinctive feature of our approach is the existence of an inflection point in the log-log plots of the conductance vs temperature, at gate voltages corresponding to peaks in the oscillation of the exponent. Moreover, we evaluate the effects of a transverse magnetic field on the transport properties of the multiwalled nanotubes. For fields of the order of 4 T, we find changes in the band structure that may be already significant for the outer shells, leading to an appreciable variation in the power-law behavior of the conductance. We then foresee the appearance of sizeable modulations in the exponent of the conductance for higher magnetic fields, as the different subbands are shifted towards the development of flat Landau levels. © 2006 The American Physical Society.J.G. acknowledges the financial support of the Ministerio de Educación y Ciencia Spain through Grant No. BFM2003-05317. E.P. was also supported by INFN Grant No. 10068.Peer Reviewe

Influence of dimensionality on superconductivity in carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes (CNs), looking for the break-down of the one dimensional Luttinger liquid regime due to the strong screening of the long-range part of the Coulomb repulsion. We show that such a breakdown is realized both in ultra-small single wall CNs and multi wall CNs, while a purely electronic mechanism could explain the superconductivity (SC) observed recently in ultra-small (diameter $\sim 0.4 nm$) single wall CNs ($T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$). We show that both the doping and the screening of long-range part of the electron-electron repulsion, needed to allow the SC phase, are related to the intrinsically 3D nature of the environment where the CNs operate.Comment: 5 pages, 3 figures, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in J. Phys. Cond. Ma