Related papers: On the non-existence of zero modes
A Weyl semimetal has Weyl nodes that always come in pairs with opposite chiralities. Notably, different ways of connection between nodes are possible and would lead to distinct topologies. Here we identify their differences in many respects…
We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials…
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…
Weyl semimetals are three-dimensional topological states of matter, in a sense that they host paired monopoles and antimonopoles of Berry curvature in momentum space, leading to the chiral anomaly. The chiral anomaly has long been believed…
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…
We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In a suitable torus…
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…
Conditions for the existence of shear-free and expansion-free non-null vector fields in spaces with affine connections and metrics are found. On their basis Weyl's spaces with shear-free and expansion-free conformal Killing vectors are…
We show that the Dirac operator on a spin manifold does not admit $L^2$ eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if…
We find that the zero mode($q^{+}=0$ mode of a continuum theory) contribution is crucial to obtain the correct values of the light-front current $J^{-}$ in the Drell-Yan($q^{+}=0$) frame. In the exactly solvable model of (1+1)-dimensional…
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the…
We study the conformal classes of 2-dimensional Lorentzian tori with (non zero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite…
Semiconductor nanowires with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana…
For the non-perturbative analysis of the topological content of Yang-Mills theories, it is essential to disentangle long-range structures from short-range fluctuations. Some time ago, one of us proposed to use the adjoint modes of the Dirac…
We present a result for non-compact manifolds with invertible Dirac operator, where we link the presence of a massless Killing spinor, with a harmonic, closed conformal Killing-Yano tensor, if one exists for the specic manifold. A couple of…
We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…
Weyl degeneracies in spectra of magnetoplasma waves enable nonreciprocal energy flow and topologically protected modes, yet conventional materials require impractical magnetic fields to operate. Developing an effective Hamiltonian framework…
Among the many far-reaching consequences of the potential existence of a magnetic monopole, it induces topological zero modes in the Dirac equation, which were derived by Jackiw and Rebbi 46 years ago and have been elusive ever since. Here,…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…
The IKKT model is proposed as a non-perturbative formulation of superstring theory. We propose a Dirac operator on the noncommutative torus,which is consistent with the IKKT model, based on noncommutative geometry. Next, we consider…