On the Coulomb interaction in chiral-invariant one-dimensional electron systems

We consider a one-dimensional electron system, suitable for the description of the electronic correlations in a metallic carbon nanotube. Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction between currents of well-defined chirality. In the limit of a very large number n of subbands we find a strong renormalization of the Fermi velocity, reminiscent of a similar phenomenon in the graphite sheet. For small n or sufficiently low energy, the Luttinger liquid behavior takes over, with a strong wavefunction renormalization leading to a vanishing quasiparticle weight. Our approach is appropriate to study the crossover from two-dimensional to one-dimensional behavior in carbon nanotubes of large radius.Comment: 8 pages, 2 figures, LaTeX, PACS: 71.27.+a, 73.20.D, 05.30.F

Crossover from marginal Fermi liquid to Luttinger liquid behavior in carbon nanotubes

We study graphene-based electron systems with long-range Coulomb interaction by performing an analytic continuation in the number of dimensions. We characterize in this way the crossover between the marginal Fermi liquid behavior of a graphite layer and the Luttinger liquid behavior at $D = 1$. The former persists for any dimension above $D = 1$. However, the proximity to the $D = 1$ fixed-point strongly influences the phenomenology of quasi-onedimensional systems, giving rise to an effective power-law behavior of observables like the density of states. This applies to nanotubes of large radius, for which we predict a lower bound of the corresponding exponent that turns out to be very close to the value measured in multi-walled nanotubes.Comment: 4 pages, 4 postscript figure

Large N Effects and Renormalization of the Long-Range Coulomb Interaction in Carbon Nanotubes

We develop a dimensional regularization approach to deal with the low-energy effects of the long-range Coulomb interaction in 1D electron systems. The method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1, providing at the same time insight about the fixed-points of the theory. We show that the effect of increasing the number N of subbands at the Fermi level is opposite to that of approaching the bare Coulomb interaction in the limit D --> 1. Then, we devise a double scaling limit, in which the large N effects are able to tame the singularities due to the long-range interaction. Thus, regular expressions can be obtained for all observables right at D = 1, bearing also a dependence o the doping level of the system. Our results imply a variation with N in the value of the exponent for the tunneling density of states, which is in fair agreement with that observed in different transport experiments involving carbon nanotubes. As the doping level is increased in nanotubes of large radius and multi-walled nanotubes, we predict a significant reduction of order N^{-1/2} in the critical exponent of the tunneling density of states.Comment: 16 pages, 5 figures, PACS codes: 73.40, 11.10.

Cluster of galaxies around seven radio-loud QSOs at 1<z<1.6: K-band images

We have conducted a NIR study of the environments of seven radio-loud quasars at redshifts 1<z<1.6. In present paper we describe deep $K$ band images obtained for the fields of ~6X6 arcmin around the quasars with 3$\sigma$ limiting magnitudes of K~20.5. These fields were previously studied using deep B and R band images (Sanchez & Gonzalez-Serrano 1999). Using together optical and NIR data, it has been found a significant excess of galaxies which optical-NIR colours, luminosity, spatial scale, and number of galaxies are compatible with clusters at the redshift of the quasar. We have selected a sample of cluster candidates analyzing the R-K vs. K diagram. A ~25% of the candidates present red optical-NIR colours and an ultraviolet excess. This population has been also found in clusters around quasars at the same redshifts (Tanaka et al. 2000; Haines et al. 2001). These galaxies seem to follow a mixed evolution: a main passive evolution plus late starformation processes. The quasars do not inhabit the core of the clusters, being found in the outer regions. This result agrees with the hypothesis that the origin/feeding mechanism of the nuclear activity were merging processes. The quasars inhabit the region were a collision is most probably to produce a merger.Comment: 15 pages. A&A, accepted for publishin

Copper(I)-Phosphinite Complexes in Click Cycloadditions: Three-Component Reactions and Preparation of 5-Iodotriazoles

© 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.The remarkable activity displayed by copper(I)–phosphinite complexes of general formula [CuBr(L)] in two challenging cycloadditions is reported: a) the one-pot azidonation/cycloaddition of boronic acids, NaN3, and terminal alkynes; b) the cycloaddition of azides and iodoalkynes. These air-stable catalysts led to very good results in both cases and the expected triazoles could be isolated in pure form under ‘Click-suitable’ conditions