arXiv subjects

F. Moraes

Publications and source records attributed to F. Moraes.

At least 19 recordsLinked to original sources

arXiv2023

An Abelian Higgs model for disclinations in nematics

Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line defects of zero width corresponding to a singularity of the curvature in an otherwise flat background. On the other hand, in two dimensions, the Frank free energy of a nematic liquid crystal may be interpreted as an Abelian Higgs Lagrangian. In this work, we construct an Abelian Higgs model coupled to "gravity" for the nematic phase, with the perspective of finding more realistic disclinations. That is, a cylindrically symmetric line defect of finite radius, invariant under translations along its axis. Numerical analysis of the equations of motion indeed yield a $+1$ winding number "thick" disclination. The defect is described jointly by the gauge and the Higgs fields, that compose the director field, and the background geometry. Away from the defect, the geometry is conical, associated to a dihedral deficit angle. The gauge field, confined to the defect, gives a structure to the disclination while the Higgs field, outside, represents the nematic order.

cond-mat.soft↗

arXiv2023

Metamaterial branes

In this article, we propose metamaterials analog brane models based on the geometric optics approach. We show how to model the Randall-Sundrum thin brane model and the Gremm model for a thick brane. We incorporate the Yukawa-like confinement mechanics for thick branes in the analog system and show an asymmetrical analog brane model with and without the confinement mechanisms.

hep-th↗

arXiv2021

Geometric effects on the electronic structure of curved nanotubes and curved graphene: the case of the helix, catenary, helicoid, and catenoid

Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative description of the conduction electrons' behavior. The confinement process of a quantum particle to a curve or surface leads us, in the so-called "confining potential formalism" (CPF), to a geometry-induced potential (GIP) in the effective Schr\"odinger equation. With these considerations, this work aims to study in detail the consequences of constraining a quantum particle to a helix, catenary, helicoid, or catenoid, exploring the relations between these curves and surfaces using differential geometry. Initially, we use the variational method to estimate the energy of the particle in its ground state, and thus, we obtain better approximations with the use of the confluent Heun function through numerical calculations. Thus, we conclude that a quantum particle constrained to an infinite helix has its angular momentum quantized due to the geometry of the curve, while in the cases of the catenary, helicoid, and catenoid the particle can be found either in a single bound state or in excited states which constitute a continuous energy band. Additionally, we propose measurements of physical observables capable of discriminating the topologies of the studied surfaces, in the context of topological metrology.

cond-mat.mes-hall↗

arXiv2020

Implications of Kleinian relativity

Inspired in metamaterials, we present a covariant mechanics for particles in Kleinian spacetime and show some of its effects, such as time contraction and length dilatation. We present the new expressions for relativistic momentum and energy for a point-like particle. To illustrate the new mechanics, we describe the particle motion under a uniform Newtonian gravitational field. We also revisit the free spin-half particle problem in Kleinian spacetime, discuss some quantum implications, like the constraint on the dispersion relation for Weyl fermions, and adapt a metamaterial analog system to Klein spacetime.

gr-qc↗

arXiv2020

On the energy of topological defect lattices

Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are, therefore, a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.

cond-mat.mes-hall↗

arXiv2020

Evidence for flat zero-energy bands in bilayer graphene with a periodic defect lattice

In this work, we perform ab initio calculations, based on the density functional theory, of the effects on the graphene bilayer when we intercalate carbon atoms between the layers. We use the unit cell of the bilayer to construct larger unit cells (supercells), positioning a single carbon atom in the hollow position between the monolayers and periodically replicating the supercell. By increasing the size of the unit cell and consequently, the periodicity of the inserted atoms, we are able to minimize the carbon-carbon interaction and therefore infer the changes in the electronic, vibrational and thermal behavior of the bilayer when the intercalated atoms do not interact with each other. The main result, concerning the electronic properties, is the appearance of a doubly degenerate flat band at the Fermi level. These states are interpreted as coming from the periodic deformation of the bilayer due to the inserted atoms. It acts as a non-Abelian flux network creating zero energy at bands as predicted by San-Jose, González and Guinea in 2012. Since the periodic strain field associated to the defect array has such a strong influence on the electronic properties of the bilayer, it may be useful for practical applications. For instance, it can act as frozen-in magnetic-like field flux tubes. All-carbon nanostructures can then be designed to have electronic behavior at different regions tailored by the chosen defect pattern.

cond-mat.mes-hall↗

arXiv2018

Electronic properties of single and double napped carbon nanocones

In this paper we study the electronic properties of carbon nanocones with one and two nappes, with pentagonal and heptagonal defects in their lattices. We use the continuum model, which is based on a Dirac-like Hamiltonian with the topological effects described by localized non-Abelian gauge field fluxes. We develop a geometrical approach that can describe the two nappes of the double cone surface simultaneously, by extending the radial coordinate to the complete set of real numbers. We show that, for some combinations of different nanocones, forming the double conical surface, the local density of states near the apex of the cone does not vanish at the Fermi energy and presents a strong dependence on the angular momentum. We also obtain the energy spectrum for finite-sized nanocones and verify that it depends on the choice of topological defect on the surface, which suggests that a double nanocone can be used to control the electronic transport in carbon-based electronic devices.

cond-mat.mes-hall↗

arXiv2016

Principles of thermal design with nematic liquid crystals

Highly engineered materials are arousing great interest because of their ability to manipulate heat, as described by coordinate transformation approach. Based on the recently developed analog gravity models, this paper presents how a simple device based on nematic liquid crystal can achieve in principle either thermal concentration or expulsion. These outcomings are shown to stem from topological properties of a disclination-like structure, induced in the nematic by anchoring conditions.

cond-mat.soft↗

arXiv2015

Inertial-Hall effect: the influence of rotation on the Hall conductivity

Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. In this paper, we consider a rotating non-interacting planar two-dimensional electron gas with a perpendicular uniform magnetic field and investigate the effects of the rotation in the Hall conductivi

cond-mat.mes-hall↗

arXiv2014

Indirect band gap in graphene from modulation of the Fermi velocity

In this work we study theoretically the electronic properties of a sheet of graphene grown on a periodic heterostructure substrate. We write an effective Dirac equation, which includes a dependence of both the band gap and the Fermi velocity on the position, due to the influence of the substrate. This way, both bandgap and Fermi velocity enter the Dirac equation as operators. The Dirac equation is solved exactly and we find the superlattice minibands with gaps due to the breaking of translational symmetry induced by the underlying heterostructure. The spatial dependence of the Fermi velocity makes the band gap be indirect, bringing about interesting possibilities for applications in the design of nanoelectronic devices. In the limit of constant Fermi velocity we obtain a band structure, with direct band gap, very close to the one previously found in the literature, obtained using the transfer matrix method.

cond-mat.mtrl-sci↗

arXiv2014

Effects of rotation in the energy spectrum of $C_{60}$

In this paper, motivated by the experimental evidence of rapidly rotating $C_{60}$ molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static $C_{60}$ are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

cond-mat.mes-hall↗

arXiv2014

Landau levels, self-adjoint extensions and Hall conductivity on a cone

In this work we obtain the Landau levels and the Hall conductivity at zero temperature of a two-dimensional electron gas on a conical surface. We investigate the integer quantum Hall effect considering two different approaches. The first one is an extrinsic approach which employs an effective scalar potential that contains both the Gaussian and the mean curvature of the surface. The second one, an intrinsic approach where the Gaussian curvature is the sole term in the scalar curvature potential. From a theoretical point of view, the singular Gaussian curvature of the cone may affect the wave functions and the respective Landau levels. Since this problem requests {\it self-adjoint extensions}, we investigate how the conical tip could influence the integer quantum Hall effect, comparing with the case were the coupling between the wave functions and the conical tip is ignored. This last case corresponds to the so-called {\it Friedrichs extension}. In all cases, the Hall conductivity is enhanced by the conical geometry depending on the opening angle. There are a considerable number of theoretical papers concerned with the self-adjoint extensions on a cone and now we hope the work addressed here inspires experimental investigation on these questions about quantum dynamics on a cone.

cond-mat.mes-hall↗

arXiv2013

Metric approach for sound propagation in nematic liquid crystals

In the eikonal approach, we describe sound propagation near to topological defects of nematic liquid crystal as geodesics of a non-euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermat's principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve informations about the elastic constants.

cond-mat.soft↗

arXiv2012

Threading dislocation densities in semiconductor crystals: a geometric approach

In this letter, we introduce a geometric model to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show that a uniform distribution of screw dislocations acts as an effective uniform magnetic field which yields bound states for a spin-half quantum particle, even in the presence of a repulsive Coulomb-like potential. This introduces energy levels within the band gap, increasing the carrier concentration in the region threaded by the dislocation density and adding additional recombination paths other than the near band-edge recombination.

quant-ph↗

arXiv2012

Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux

The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.

hep-th↗

arXiv2010

Electric field induced inversion of the sign of half-integer disclinations in 2D nematic liquid crystals

We study the effect of the rotation of an external electric field on the dynamics of half-integer disclination networks in two dimensional nematic liquid crystals with a negative dielectric anisotropy using LICRA, a LIquid CRystal Algorithm developed by the authors. We show that a rotation of $π$ of the electric field around an axis of the liquid crystal plane continuously transforms all half-integer disclinations of the network into disclinations of opposite sign via twist disclinations. We also determine the evolution of the characteristic length scale, thus quantifying the impact of the external electric field on the coarsening of the defect network.

cond-mat.soft↗

arXiv2010

Diffraction of light by topological defects in liquid crystals

We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the global monopole and cosmic string geometries. We obtain the scattering amplitude and the differential and total scattering cross section for the case of the hedgehog defect, in terms of the characteristic parameters of the liquid crystal. Studying the disclination case, a cylindrical partial wave method is developed. As an application of the previous developments, we also examine the temperature influence on the localization of the diffraction patterns.

cond-mat.soft↗

arXiv2010

Nematic liquid crystal dynamics under applied electric fields

In this paper we investigate the dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available LIquid CRystal Algorithm (LICRA) developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.

cond-mat.soft↗