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

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.

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

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

Quantum Hall effect in carbon nanotubes and curved graphene strips

8 págs.; 7 figs. ; PACS number s : 73.22. f, 73.43. f, 75.75. aWe develop a long-wavelength approximation in order to describe the low-energy states of carbon nanotubes in a transverse magnetic field. We show that in the limit where the square of the magnetic length l= c eB is much larger than the C-C distance times the nanotube radius R, the low-energy theory is given by the linear coupling of a two-component Dirac spinor to the corresponding vector potential. We investigate in this regime the evolution of the band structure of zigzag nanotubes for values of R l>1, showing that for radius R≈20 nm a clear pattern of Landau levels starts to develop for magnetic field strength B 10 T. The levels tend to be fourfold degenerate, and we clarify the transition to the typical twofold degeneracy of graphene as the nanotube is unrolled to form a curved strip. We show that the dynamics of the Dirac fermions leads to states which are localized at the flanks of the nanotube and that carry chiral currents in the longitudinal direction. We discuss the possibility of observing the quantization of the Hall conductivity in thick carbon nanotubes, which should display steps at even multiples of 2 e2 h, with values doubled with respect to those in the odd-integer quantization of graphene. © 2007 The American Physical Society.The financial support of the Ministerio de Educación y Ciencia Spain through Grants Nos. FIS2005-05478-C02- 01/02 and INFN 05-14 is gratefully acknowledged. F.G. acknowledges funding from the European Union under Contract No. 12881 NEST. S.B. and P.O. acknowledge the support of the grant 2006 PRIN “Sistemi Quantistici Macroscopici-Aspetti Fondamentali ed Applicazioni di strutture Josephson Non Convenzionali.” E.P. was also supported by INFN under Grant No. 10068.Peer Reviewe

On the ab initio calculation of CVV Auger spectra in closed-shell systems

We propose an ab initio method to evaluate the core-valence-valence (CVV) Auger spectrum of systems with filled valence bands. The method is based on the Cini-Sawatzky theory, and aims at estimating the parameters by first-principles calculations in the framework of density-functional theory (DFT). Photoemission energies and the interaction energy for the two holes in the final state are evaluated by performing DFT simulations for the system with varied population of electronic levels. Transition matrix elements are taken from atomic results. The approach takes into account the non-sphericity of the density of states of the emitting atom, spin-orbit interaction in core and valence, and non quadratic terms in the total energy expansion with respect to fractional occupation numbers. It is tested on two benchmark systems, Zn and Cu metals, leading in both cases to L23M45M45 Auger peaks within 2 eV from the experimental ones. Detailed analysis is presented on the relative weight of the various contributions considered in our method, providing the basis for future development. Especially problematic is the evaluation of the hole-hole interaction for systems with broad valence bands: our method underestimates its value in Cu, while we obtain excellent results for this quantity in Zn.Comment: 20 pages, 5 figures, 4 table

"Spin-Disentangled" Exact Diagonalization of Repulsive Hubbard Systems: Superconducting Pair Propagation

By a novel exact diagonalization technique we show that bound pairs propagate between repulsive Hubbard clusters in a superconducting fashion. The size of the matrices that must be handled depends on the number of fermion configurations {\em per spin}, which is of the order of the square root of the overall size of the Hilbert space. We use CuO$_{4}$ units connected by weak O-O links to model interplanar coupling and c-axis superconductivity in Cuprates. The numerical evidence on Cu$_{2}$O$_{8}$ and Cu$_{3}$O$_{12}$ prompts a new analytic scheme describing the propagation of bound pairs and also the superconducting flux quantization in a 3-d geometry.Comment: 5 pages, 3 figure

Time-dependent quantum transport with superconducting leads: a discrete basis Kohn-Sham formulation and propagation scheme

In this work we put forward an exact one-particle framework to study nano-scale Josephson junctions out of equilibrium and propose a propagation scheme to calculate the time-dependent current in response to an external applied bias. Using a discrete basis set and Peierls phases for the electromagnetic field we prove that the current and pairing densities in a superconducting system of interacting electrons can be reproduced in a non-interacting Kohn-Sham (KS) system under the influence of different Peierls phases {\em and} of a pairing field. An extended Keldysh formalism for the non-equilibrium Nambu-Green's function (NEGF) is then introduced to calculate the short- and long-time response of the KS system. The equivalence between the NEGF approach and a combination of the static and time-dependent Bogoliubov-deGennes (BdG) equations is shown. For systems consisting of a finite region coupled to ${\cal N}$ superconducting semi-infinite leads we numerically solve the static BdG equations with a generalized wave-guide approach and their time-dependent version with an embedded Crank-Nicholson scheme. To demonstrate the feasibility of the propagation scheme we study two paradigmatic models, the single-level quantum dot and a tight-binding chain, under dc, ac and pulse biases. We provide a time-dependent picture of single and multiple Andreev reflections, show that Andreev bound states can be exploited to generate a zero-bias ac current of tunable frequency, and find a long-living resonant effect induced by microwave irradiation of appropriate frequency.Comment: 20 pages, 9 figures, published versio