Introduction to topological defects: from liquid crystals to particle physics

Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction, which locally defines an orientational order. Sometimes, this order is broken and singularities appear in the form of topological defects. This tutorial article is dedicated to the geometry, topology and physics of these defects. We introduce the main models used to describe the nematic phase and discuss the isotropic-nematic phase transition. Then, we present the different families of defects in nematics and examine some of their physical outcomes. Finally, we show that topological defects are universal patterns of nature, appearing not only in soft matter, but also in biology, cosmology, geology and even particle physics.Comment: 40 pages, 9 figures, review pape

Geometric theory of topological defects: methodological developments and new trends

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena

On the possibility of classical vacuum polarization and magnetization

It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the magnetic flux density ($\bf{B}$) vectors (up to the constant $\mu_0^{-1}$). The fact that gravity may change this by effectively inducing dielectric or magnetic responses to the primary fields is commonly overlooked. It is the purpose of this communication to call attention to classical polarization or magnetization of the vacuum due to the concomitant presence of gravitational and electromagnetic sources. The formalism of differential forms (exterior calculus) is used since it provides a clear-cut way to achieve this. This work offers new routes for possible detection of various spacetime geometries via their electromagnetic manifestations and the way they influence light propagation

Using torsion to manipulate spin currents

We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a single screw dislocation, whose Burgers vector measures the torsion amplitude. The problem, first treated in the relativistic limit describing fermions that couple minimally to torsion, is then analysed in the Pauli limit We show that torsion induces a geometric potential and also that it couples generically to the phase of the wave function, giving rise to the possibility of using torsion to manipulate spin currents in the case of spinor wave functions. These results emerge as an alternative strategy for using screw dislocations in the design of spintronic-based devices

Magnetic and geometric effects on the electronic transport of metallic nanotubes

The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons.Comment: The following article has been accepted by J. of Applied Physic