Related papers: Magnetic Zero-Modes, Vortices and Cartan Geometry
We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure…
We discuss that the singularities appearing in Dirac's formulation of magnetic monopoles are due to the set of fields which he used and not due to the physical properties of magnetic monopoles. We explain in detail that we can find the same…
We study a time-reversal invariant vortex, namely a spin vortex, in helical superconductors by focusing on its emergent gravitational structure. The topology of the time-reversal invariant vortex is classified by a $\mathbb{Z}_2$ invariant:…
We give a gauge-invariant definition of the vortex surface in SU(N) Yang-Mills theory without using the gauge fixing procedure. In this construction, gauge-invariant magnetic monopoles with fractional magnetic charges emerge in the boundary…
Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical…
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double…
In this paper, we study the relation of the sign of the Gaussian and mean curvature of modular surfaces in Lorentz-Minkowski $3$-space to the zeroes of the associated complex analytic functions and its derivatives. Further, we completely…
We study 2-dimensional submanifolds of the space ${\mathbb{L}}({\mathbb{H}}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral K\"ahler structure. Such a surface is Lagrangian iff there exists a surface in…
We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a…
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical…
We propose a simple scenario to describe a dislocation-induced Majorana zero mode on the surface of an iron-based superconductor, using an illustrative model with a cylindrical hole of radius $R$ perpendicular to its top surface.…
We use the overlap formalism to define a topological index on the lattice. We study the spectral flow of the hermitian Wilson-Dirac operator and identify zero crossings with topological objects. We determine the topological susceptibility…
Magnetic skyrmions in proximity to superconductors offer a route to engineering topological superconductivity due to the synthetic spin-orbit coupling engendered by the spin twist of the skyrmion texture. Previous theoretical works show…
It is well-known that macroscopically-normalizable zero-energy wavefunctions of spin-$\frac{1}{2}$ particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of…
In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as compact…
Rotating magnetic structures are common in astrophysics, from vortex tubes and tornados in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure and…
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the…
We study a generalization of the Callan-Harvey mechanism to the case of a non local mass. Using a 2+1 model as a concrete example, we show that both the existence and properties of localized zero modes can also be consistently studied when…
In the large flux limit vortices become flux tubes with almost constant magnetic field in the interior region. This occurs in the case of non-Abelian vortices as well, and the study of such configurations allows us to reveal a close…
We demonstrate that it is conceptually and computationally favorable to regard spin-weighted spherical harmonics as vector valued functions on the total space $SO(3)$ of the Hopf bundle, satisfying a covariance condition with respect to the…