Properties of electrons near a Van Hove singularity

The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.Comment: Proceedings of SNS-01 to appear in the Journal of Physics and Chemistry of Solids, SNS-0

Variational approach to the Hubbard model in a C60 cluster

5 págs.; 4 figs.; 3 tabs.We propose a computational scheme for the Hubbard model in the C60 cluster in which the interaction with the Fermi sea of charges added to the neutral molecule is switched on sequentially. This is applied to the calculation of the balance of charging energies, within a low-energy truncation of the space of states which produces moderate errors for an intermediate range of the interaction strength. ©1996 American Physical SocietyPeer Reviewe

Phase diagram of carbon nanotube ropes

14 págs.; 9 figs.; 1 tab. ; PACS number(s): 71.20.Tx, 71.10.Pm, 74.50.1rThe zero-temperature phase diagram of carbon nanotube ropes is studied using a computational framework that incorporates the renormalization of intratube interactions and the effect of intertube Coulomb screening. This allows us to undertake a systematic analysis as a function of the number of metallic nanotubes in the rope and the effective strength of the phonon-mediated interaction. We find that there is in general a weak-coupling regime of the interactions, corresponding to Luttinger-liquid behavior in thin ropes and to superconducting behavior in sufficiently thick ropes. Furthermore, we show the existence of exotic phases in the strong-coupling regime, characterized by the appearance of charge instabilities that depend on the helicity and the doping level of the nanotubes in the rope. Our approach allows for the simultaneous analysis of the scaling of the Cooper-pair tunneling amplitude between metallic nanotubes, making it possible to discern the crossover from purely one-dimensional physics to the setting of three-dimensional Cooper-pair coherence. We provide then good estimates of the superconducting transition temperature and discuss the connection of our results with recent experiments. ©2004 American Physical SocietyJ. V. A. acknowledges support from S. Moukouri and stimulating discussions with J. Allen. J. G. acknowledges financial support from the Ministerio de Ciencia y Tecnología Grant No. BFM2003-05317.Peer Reviewe

Electronic instabilities in 3D arrays of small-diameter (3,3) carbon nanotubes

We investigate the electronic instabilities of the small-diameter (3,3) carbon nanotubes by studying the low-energy perturbations of the normal Luttinger liquid regime. The bosonization approach is adopted to deal exactly with the interactions in the forward-scattering channels, while renormalization group methods are used to analyze the low-energy instabilities. In this respect, we take into account the competition between the effective e-e interaction mediated by phonons and the Coulomb interaction in backscattering and Umklapp channels. Moreover, we apply our analysis to relevant experimental conditions where the nanotubes are assembled into large three-dimensional arrays, which leads to an efficient screening of the Coulomb potential at small momentum-transfer. We find that the destabilization of the normal metallic behavior takes place through the onset of critical behavior in some of the two charge stiffnesses that characterize the Luttinger liquid state. From a physical point of view, this results in either a divergent compressibility or a vanishing renormalized velocity for current excitations at the point of the transition. We observe anyhow that this kind of critical behavior occurs without the development of any appreciable sign of superconducting correlations.Comment: 10 pages, 12 figure

Integration of biophysical connectivity in the spatial optimization of coastal ecosystem services

Ecological connectivity in coastal oceanic waters is mediated by dispersion of the early life stages of marine organisms and conditions the structure of biological communities and the provision of ecosystem services. Integrated management strategies aimed at ensuring long-term service provision to society do not currently consider the importance of dispersal and larval connectivity. A spatial optimization model is introduced to maximise the potential provision of ecosystem services in coastal areas by accounting for the role of dispersal and larval connectivity. The approach combines a validated coastal circulation model that reproduces realistic patterns of larval transport along the coast, which ultimately conditions the biological connectivity and productivity of an area, with additional spatial layers describing potential ecosystem services. The spatial optimization exercise was tested along the coast of Central Chile, a highly productive area dominated by the Humboldt Current. Results show it is unnecessary to relocate existing management areas, as increasing no-take areas by 10% could maximise ecosystem service provision, while improving the spatial representativeness of protected areas and minimizing social conflicts. The location of protected areas was underrepresented in some sections of the study domain, principally due to the restriction of the model to rocky subtidal habitats. Future model developments should encompass the diversity of coastal ecosystems and human activities to inform integrative spatial management. Nevertheless, the spatial optimization model is innovative not only for its integrated ecosystem perspective, but also because it demonstrates that it is possible to incorporate time-varying biophysical connectivity within the optimization problem, thereby linking the dynamics of exploited populations produced by the spatial management regime.Comment: 30 pages, 5 figures, 2 tables; 1 graphical abstract. In this version: numbering of figures corrected, updated figure 2, typos corrected and references fixe

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results has been clarifie

Deformation of the Fermi surface in the extended Hubbard model

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies producing deformations of the Fermi surface which break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuck instability competes with ferromagnetism and is suppressed at a critical value of U(V). The interaction V renormalizes the t' parameter to smaller values what favours nesting. It also induces changes on the topology of the Fermi surface which can go from hole to electron-like what may explain recent ARPES experiments.Comment: 5 pages, 4 ps figure

Fermi surface renormalization in Hubbard ladders

We derive the one-loop renormalization equations for the shift in the Fermi-wavevectors for one-dimensional interacting models with four Fermi-points (two left and two right movers) and two Fermi velocities v_1 and v_2. We find the shift to be proportional to (v_1-v_2)U^2, where U is the Hubbard-U. Our results apply to the Hubbard ladder and to the t_1-t_2 Hubbard model. The Fermi-sea with fewer particles tends to empty. The stability of a saddle point due to shifts of the Fermi-energy and the shift of the Fermi-wavevector at the Mott-Hubbard transition are discussed.Comment: 5 pages, 4 Postscript figure

Kinematics of electrons near a Van Hove singularity

A two dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities, and it is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of the electron scattering in this model. The similitudes, and differences, between a standard Renormalization Group approach and previous work based on parquet summations of log$^2$ divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.Comment: 5 pages, 3 postscript figure