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The electric field inside typical conductors drops down exponentially with the screening length determined by an intrinsic length scale of the system such as the density of mobile carriers. We show that in a classically conformal system with boundaries, where the intrinsic length scale is absent, the screening of an external electric field is governed by the quantum conformal anomaly associated with the renormalization of the electric charge. The electric field decays algebraically with a fractional power determined by the beta function of the system. We argue that this `anomalous conformal screening effect' is an indirect manifestation of the Schwinger pair production in relativistic field theory. We discuss the experimental feasibility of the proposed phenomenon in Dirac and Weyl semimetals what would allow direct experimental access to the beta function., Comment: 5 pages, 4 figures

We show that a conformal anomaly in Weyl/Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material., Comment: 6 pages including appendix, 1 figure

The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the metallic dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds., Comment: 75 pages, 15 figures, review article

We study the emergence of gauge couplings in the surface states of topological insulators. We show that gauge fields arise when a three dimensional strong topological insulator is coated with an easy-plane ferromagnet with magnetization parallel to the surface. We analyze the modification induced by the gauge fields on the surface spectrum for some specific magnetic configurations., Comment: We have fixed Fig. 2 b and c that were exchanged in the previous version

The physics of graphene is acting as a bridge between quantum field theory and condensed matter physics due to the special quality of the graphene quasiparticles behaving as massless two dimensional Dirac fermions. Moreover, the particular structure of the 2D crystal lattice sets the arena to study and unify concepts from elasticity, topology and cosmology. In this paper we analyze these connections combining a pedagogical, intuitive approach with a more rigorous formalism when required., Comment: Update of the manuscript published on-line in Physics Reports. 43 pages, 18 figures

We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero energy Landau levels will form, associated to the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that $h^2 / (l a) \gtrsim 1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy, and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combined effect of the ripples and an external magnetic field breaks the valley symmetry of graphene leading to the possibility of valley selection.

Graphite is a layered material showing a strong anisotropy. Among the unconventional properties reported by experiments, the electronic transport along the c-axis, which has direct implications in order to build graphitic devices, remains a controversial topic. We study the influence of inelastic scattering on the electron tunnelling between layers. In the presence of electron electron interactions, tunnelling processes are modified by inelastic scattering events., Comment: 9 pages, no figures Proceedings of the Graphene Conference, MPI PKS Dresden, September 2006

We study the changes in the electronic structure induced by lattice defects in graphene planes. In many cases, lattice distortions give rise to localized states at the Fermi level. Electron-electron interactions lead to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic, due to the semimetallic properties of graphene, Comment: 4 pages, 4 figures

Recent experiments report the existence of ferromagnetic and superconducting fluctuations in graphite at unexpectedly high temperatures. The interplay of disorder and interactions in a 2D graphene layer is shown to give rise to a rich phase diagram where strong coupling phases can become stable. Local defects can explain the ferromagnetic signals., Comment: Presented at SNS'2004, Sitges,Spain, July 11-16,2004, being considered for publication in Jour.Phys.Chem.Solids

The out-of-plane hopping in layered metals with strong electronic correlation is analyzed theoretically. By studying the effects of in-plane interactions on the interlayer tunnelling we investigate one of the oldest unresolved problems of high-T$_c$ cuprates, the so-called bilayer splitting. The strong electron-electron interactions within each layer reduce the quasiparticle weight, and modify the hopping between layers. We analyze the effect of the in-plane correlations on the interlayer hopping using a Renormalization Group scheme already applied to the problem of interlayer coherence . The bilayer band splitting acquires a significant temperature and doping dependence, and can be completely suppressed when the Fermi energy coincides with a Van Hove singularity., Comment: contrbution submitted to SNS04

The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points where the strength of the interactions remains finite, as in one dimensional Luttinger liquids. These fixed points can be either stable (attractive), when the disorder is associated to topological defects in the lattice or to a random mass term, or unstable (repulsive) when the disorder is induced by impurities outside the graphene planes. In addition, we analyze mid-gap states which can arise near interfaces or vacancies., Comment: 4 pages, 3 figures

A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out--of--plane tunneling in layered metals considering different models. By studying the effects of in--plane interactions on the interlayer tunneling of electrons near the Fermi level, we establish the relation between departure from Fermi liquid behavior driven by electron correlations inside the layer and the out of plane coherence. Response functions, directly comparable with experimental data are obtained.

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-01

The effects of the electron-electron interactions in a graphene layer are investigated. It is shown that short range couplings are irrelevant, and scale towards zero at low energies, due to the vanishing of density of states at the Fermi level. Topological disorder enhances the density of states, and can lead to instabilities. In the presence of sufficiently strong repulsive interactions, p-wave superconductivity can emerge., Comment: 8 pages

The instabilities induced on a two-dimensional system of correlated electrons by the anisotropies of its Fermi line are analyzed on general grounds. Simple scaling arguments allow to predict the opening of a superconducting gap with a well-defined symmetry prescribed by the geometry of the Fermi line. The same arguments predict a critical dimension of 3/2 for the transition of the two-dimensional system to non-Fermi liquid behavior. The methods are applied to the t-t' Hubbard model in a wide range of dopings., Comment: 25 pages, 13 postscript figures

The magnetic properties of the t-t' Hubbard Model in the two dimensional square lattice are studied within an unrestricted Hartree-Fock approximation in real space. The interplay between antiferromagnetism, ferromagnetism, phase separation and inhomogeneous magnetic textures is studied. It is shown that, at sufficiently large values of t'/t, a rich fenomenology is to be expected between the antiferromagnetic phase at half filling and the ferromagnetic phase a lower fillings., Comment: 13 pages, 10 figures

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 figures

A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed-point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi liquid and non-Fermi liquid regimes., Comment: 7 pages, 2 Postscript figures

The renormalization group approach to correlated fermions is used to determine the phase diagram of the oxide cuprates modeled by the t-t' Hubbard model at the Van Hove filling. Spin-dependent interactions give rise to instabilities corresponding to ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space., Comment: Latex, 39 pages,12 figures

We apply a renormalization group approach to the determination of the phase diagram of the t-t' Hubbard model at the Van Hove filling, as function of t'/t, for small values of U/t. The model presents ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space., Comment: 5 pages, revtex, 4 postscript figures in separate files

The effect of strong anisotropy on the Fermi line of a system of correlated electrons is studied in two space dimensions, using renormalization group techniques. Inflection points change the scaling exponents of the couplings, enhancing the instabilities of the system. They increase the critical dimension for non Fermi liquid behavior, from 1 to 3/2. Assuming that, in the absence of nesting, the dominant instability is towards a superconducting ground state, simple rules to discern between d-wave and extended s-wave symmetry of the order parameter are given., Comment: 5 pages, revtex

The influence of electron-electron scattering on quasiparticle lifetimes in graphite is calculated. In the limit when the Fermi surface is reduced to isolated points in the Brillouin Zone, the suppression of screening leads to non Fermi liquid behavior. The inverse lifetime increases linearly with energy, in agreement with recent experiments. Similar features should also be present in narrow gap semiconductors, and in carbon nanotubes., Comment: Latex file (4 pages) + 4 figures (postscript)

We study by means of renormalization group techniques the effect that on the two-dimensional electron liquid may have the van Hove singularities observed experimentally in the copper-oxide superconductors. We find significant deviations from Fermi liquid behavior, that lead to the appearance of an unstable fixed point in the renormalization group flow of the effective coupling constant. Besides the attenuation of electron quasiparticles already known on phenomenological grounds, our approach is able to explain the reduction in the dispersion of the band as well as the pinning of the Fermi level near the singularity, as observed in the photoemission experiments., Comment: Latex manuscript, 29 pages, 4 postcript figures

This entry has been removed since we are an archive and not an advertisement space., Comment: LATEX file, 7 pages, no figures. This entry has been removed since we are an archive and not an advertisement space

A model of interacting two dimensional electrons near a Van Hove singularity is studied, using renormalization group techniques. In hole doped systems, the chemical potential is found to be pinned near the singularity, when the electron-electron interactions are repulsive. The RG treatment of the leading divergences appearing in perturbation theory give rise to marginal behavior and anisotropic superconductivity., Comment: 4 Latex pages + 5 postcript figures

The multiplet structure induced by the Coulomb interactions in C$_{60}^{n-}$ ($n = 1 - 12$) is analyzed. The partially ocuppied LUMO gives rise to a set of levels which fill a relatively wide band ( $\approx 2-3$ eV ). A large ($\sim 1$ eV) intramolecular effective repulsion is found. The anions are also shown to be highly polarizable. The optical absorption and photoemission spectra are calculated. The probability of exciting the molecule upon the addition or removal of one electron is shown to be significant, and this effect may give rise to the insulating behavior of K$_4$C$_{60}$. The role of intermolecular interactions in suppressing the net repulsion within the C$_{60}$ molecules is discussed., Comment: 9 pages + 1 postscript figure

A system of electrons in the two-dimensional honeycomb lattice with Coulomb interactions is described by a renormalizable quantum field theory similar but not equal to QED_3. Renormalization group techniques are used to investigate the infrared behaviour of the system that flows to a fixed point with non-Fermi liquid characteristics. There are anomalous dimensions in the fermionic observables, no quasiparticle pole, and anomalous screening of the Coulomb interaction. These results are robust as the Fermi level is not changed by the interaction. The system resembles in the infrared the one-dimensional Luttinger liquid., Comment: 23 pages, LaTeX file (7 figures not included available upon request), IEM-TH-54/93

We study the Coulomb interactions in fullerene molecules within a continuum formalism. The model gives rise to a renormalizable field theory, which has many similarities to standard quantum electrodynamics. The effective electric charge at low energies is reduced by screening processes. The associated renormalization of the one electron Green's function leads to the vanishing of the quasiparticle pole. It implies the dissappearance of coherent one particle excitations, in close analogy to the one dimensional Luttinger liquid. The relevance of these results for C$_{60}$ and related molecules is discussed., Comment: Revtex. 2 pages. Figures upon request

The screening properties of fullerene molecules are described by means of a continuum model which uses the electronic wavefunctions of planar graphite as a starting point. The long distance behavior of the system gives rise to a renormalizable theory, which flows towards a non trivial fixed point. Its existence implies an anomalous dielectric constant. The screening properties are neither metallic nor insulating. Alternatively, the intramolecular screening is obtained from a simple approximation to the electronic wavefunctions. Intermolecular effects are also calculated. As a consistency check, it is shown that the observed polarizability of C$_{60}$ is well eproduced., Comment: 7 pages. Revtex

The electron-phonon and Coulomb interactions inC$_{60}$, and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections $\sim 1 - 10$ meV to the electronic energies for C$_{60}$, and scales as $R^{-4}$ in larger molecules. The energies associated with electrostatic interactions are of order $\sim 1 - 4$ eV, in C$_{60}$ and scale as $R^{-1}$. Charged fullerenes show enhanced electron-phonon coupling, $\sim 10$ meV, which scales as $R^{-2}$. Finally, it is argued that non only C$_{60}^{-}$, but also C$_{60}^{--}$ are highly polarizable molecules. The polarizabilities scale as $R^3$ and $R^4$, respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed., Comment: 12 pages. No figures

The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found that a Dirac equation describes the flat graphite lattice. Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center., Comment: 29 pages, 7 figures. IASSNS-HEP-92/50