Related papers: Dirac Operator Zero-modes on a Torus

The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix} 0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where $\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic or a general strictly…

We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying…

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…

Multilayer stacks of twisted optical metasurfaces are considered as a prospective platform for chiral nanophotonic devices. Such structures are primarily used for the realization of circularly polarized light sources, artificial optical…

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator…

Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy…

We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect…

We study the zero modes of the operator $H_f=D^*_fD_f$, with a Dirac type operator $D_f$, acting on the spinor bundle over a closed even dimensional Riemannian manifold $M$. The operator $D_f=D+ifI$ is a deformation of the Dirac operator…

An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of…

We classify possible boundary conditions of a 6d Dirac fermion $\Psi$ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the…

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector…

We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base…

We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…

We consider the Dirac field in polar formulation, showing that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas, that when the limit of zero chiral angle is taken the theory…

We study torus/orbifold models with magnetic flux and Wilson line background. The number of zero-modes and their profiles depend on those backgrounds. That has interesting implications from the viewpoint of particle phenomenology.

How electronic topology develops in strongly correlated systems represents a fundamental challenge in the field of quantum materials. Recent studies have advanced the characterization and diagnosis of topology in Mott insulators whose…

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac…

We find a class of Fermion zero modes of Abelian Dirac operators in three dimensional Euclidean space where the gauge potentials and the related magnetic fields are nonzero only in a finite space region.

We report on the theoretical and experimental realization of a double-zero-index elastic waveguide and on the corresponding acoustic cloacking and supercoupling effects. The proposed waveguide uses geometric tapers in order to induce…

We show that in bilayer graphene it is possible to achieve a very restrictive confinement of the massless Dirac fermions zero-modes by using inhomogeneous magnetic fields. Specifically, we show that, using a suitable nonuniform magnetic…