Minimal conductivity of rippled graphene with topological disorder

We study the transport properties of a neutral graphene sheet with curved regions induced or stabilized by topological defects. The proposed model gives rise to Dirac fermions in a random magnetic field and in the random space dependent Fermi velocity induced by the curvature. This last term leads to singular long range correlated disorder with special characteristics. The Drude minimal conductivity at zero energy is found to be inversely proportional to the density of topological disorder, a signature of diffusive behavior.Comment: 12 pages, no figure

Topological insulating phases in mono and bilayer graphene

We analyze the influence of different quadratic interactions giving rise to time reversal invariant topological insulating phases in mono and bilayer graphene. We make use of the effective action formalism to determine the dependence of the Chern Simons coefficient on the different interactions

Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell

We study spontaneous symmetry breaking in a system of spinless fermions in the Honeycomb lattice paying special emphasis to the role of an enlarged unit cell on time reversal symmetry broken phases. We use a tight binding model with nearest neighbor hopping t and Hubbard interaction V1 and V2 and extract the phase diagram as a function of electron density and interaction within a mean field variational approach. The analysis completes the previous work done in Phys. Rev. Lett. 107, 106402 (2011) where phases with non--trivial topological properties were found with only a nearest neighbor interaction V1 in the absence of charge decouplings. We see that the topological phases are suppressed by the presence of metallic charge density fluctuations. The addition of next to nearest neighbor interaction V2 restores the topological non-trivial phases

Topological Fermi liquids from Coulomb interactions in the doped Honeycomb lattice

We get an anomalous Hall metallic state in the Honeycomb lattice with nearest neighbors only arising as a spontaneously broken symmetry state from a local nearest neighbor Coulomb interaction V . The key ingredient is to enlarge the unit cell to host six atoms that permits Kekul\'e distortions and supports self-consistent currents creating non trivial magnetic configurations with total zero flux. We find within a variational mean field approach a metallic phase with broken time reversal symmetry (T) very close in parameter space to a Pomeranchuk instability. Within the T broken region the predominant configuration is an anomalous Hall phase with non zero Hall conductivity, a realization of a topological Fermi liquid. A T broken phase with zero Hall conductivity is stable in a small region of the parameter space for lower values of V

Lie conformal algebra cohomology and the variational complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.Comment: 56 page

Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

On the relativistic L-S coupling

The fact that the Dirac equation is linear in the space and time derivatives leads to the coupling of spin and orbital angular momenta that is of a pure relativistic nature. We illustrate this fact by computing the solutions of the Dirac equation in an infinite spherical well, which allows to go from the relativistic to the non-relativistic limit by just varying the radius of the well.Comment: LateX2e, 12 pages, 1 figure, accepted in Eur. J. Phy

Positive solutions to indefinite Neumann problems when the weight has positive average

We deal with positive solutions for the Neumann boundary value problem associated with the scalar second order ODE $$u" + q(t)g(u) = 0, \quad t \in [0, T],$$ where $g: [0, +\infty[\, \to \mathbb{R}$ is positive on $\,]0, +\infty[\,$ and $q(t)$ is an indefinite weight. Complementary to previous investigations in the case $\int_0^T q(t) < 0$, we provide existence results for a suitable class of weights having (small) positive mean, when $g'(x) < 0$ at infinity. Our proof relies on a shooting argument for a suitable equivalent planar system of the type $$x' = y, \qquad y' = h(x)y^2 + q(t),$$ with $h(x)$ a continuous function defined on the whole real line.Comment: 17 pages, 3 figure

Introduction: Tricksters, humour and activism

This special issue, entitled ‘The Trickster Activist in Global Humour and Comedy’, investigates the relevance of the concept of the trickster for explaining activist expressions that emanate from comedians, or that appear in comedy and humour more generally. Comedy has traditionally been viewed as an aesthetic or entertainment medium. It has often been charged with encouraging stereotype and the affirmation of mainstream audience beliefs. Despite this, we argue, there have been moments in recent history where comedians have given their performances an increased level of social and political consciousness that resonates with the public at large, or with sections of the public. Comedians, we argue, are able to reach this level of social commentary due to their potential to become tricksters. Paradoxically, the mythical trickster is a liminal entity, one that is adept at destruction as well as creation, or at conservativism as well radicalism. The articles in this issue explore the complexity of the trickster concept, showing some of the polysemy involved in the social activism enabled by comedy and humour

Charge inhomogeneities due to smooth ripples in graphene sheets

We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Green's function of the Dirac fermions in the curved surface. Curved regions modify the Fermi velocity that becomes a function of the point on the graphene surface and induce energy dependent oscillations in the local density of states around the position of the bump. The corrections are estimated to be of a few percent of the flat density at the typical energies explored in local probes such as scanning tunnel microscopy that should be able to observe the predicted correlation of the morphology with the electronics. We discuss the connection of the present work with the recent observation of charge anisotropy in graphene and propose that it can be used as an experimental test of the curvature effects.Comment: 9 pages, 5 figures. v2: Abstract and discussion about experimental consequences expande