Related papers: Fermionic zero modes in self-dual vortex backgroun…
We show that even if a lattice Dirac operator satisfies the conditions consisting of locality, free of species doublings, correct continuum behavior, $\gm5$-hermiticity and the Ginsparg-Wilson relation, it does not necessarily have exact…
We provide an argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem…
Focusing on examples of Majorana zero modes on the corners of a two-dimensional lattice, we introduce a method to find parameter regions where the Majorana modes are perfectly localized on a single site. Such a limit allows us to study the…
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
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 investigate the influence of topological charges on non-stable zero and near-zero modes of the single uni-color plane vortex pairs. We combine the uni-color plane vortices with the spherical vortex and also construct the plane vortex…
We introduce vortex configurations with fractional topological charges where one unicolor or colorful intersection of two perpendicular vortex pairs contributes to the topological charge of the configurations. Using both, the overlap and…
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…
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…
We consider a toroidal configuration of cosmic string in 3+1 dimensions in an abelian Higgs model, a compactification of the Nielsen-Olesen string. This object is classically unstable. We explicitly compute the number of permitted zero…
Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by…
We study free fermionic models that host Majorana zero modes using the Majorana orthogonal transformation, which is a type of transformation between different fermionic models under Majorana representation of complex fermions. Using…
We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass…
In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or,…
One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the question whether such multiple zero modes may exist has remained unanswered until now.…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordstr\"{o}m-anti-de Sitter gravitational background. In the chiral limit of the color…
A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the…
We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite…
Dirac fermions, subject to external magnetic fields and in the presence of mass orders that assume topologically nontrivial spatial textures such as domain wall and vortices, for example, bind robust midgap states at zero energy, the number…