Related papers: Zero modes and index theorems for non-Hermitian Di…
The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid…
In this paper we analyze a generalized Jackiw-Rebbi (J-R) model in which a massive fermion is coupled to the kink of the $\lambda\phi^4$ model as a prescribed background field. We solve this massive J-R model exactly and analytically and…
We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they…
We consider the proximity effect between Dirac states at the surface of a topological insulator and a ferromagnet with easy plane anisotropy, which is described by the \emph{XY}-model and undergoes a Berezinskii-Kosterlitz-Thouless (BKT)…
We consider fermions in the field of static monopole-like configurations in the Euclidean space-time. In all the cases considered there exists an infinite number of zero modes, labeled by frequency i\omega. The existence of such modes is a…
Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological…
Nonzero neutrino masses imply the existence of degrees of freedom and interactions beyond those in the Standard Model. A powerful indicator of what these might be is the nature of the massive neutrinos: Dirac fermions versus Majorana…
We study the bulk-boundary correspondences for zigzag ribbons (ZRs) of massless Dirac fermion in two-dimensional $\alpha$-${T}_3$ lattice. By tuning the hopping parameter $\alpha\in[0,1]$, the $\alpha$-${T}_3$ lattice interpolates between…
We have investigated the Fock-Darwin states of the massless chiral fermions confined in a graphitic parabolic quantum dot. In the light of the Klein tunneling, we have analyzed the condition for confinement of the Dirac fermions in a…
The properties of surface Dirac Fermions on a 3D topological insulator in proximity to a magnetic insulator with spatially textured magnetization are considered. We present an exact analytical treatment of the spectrum, the bound states and…
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The…
We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in…
We show by means of ab initio calculations and tight-binding modeling that an oxide system based on a honeycomb lattice can sustain topologically non-trivial states if a single orbital dominates the spectrum close to the Fermi level. In…
Topological phases have recently witnessed a rapid progress in non-Hermitian systems. Here we study a one-dimensional non-Hermitian Aubry-Andr\'e-Harper model with imaginary periodic or quasiperiodic modulations. We demonstrate that the…
Surfaces of topological insulators host a new class of states with Dirac dispersion and helical spin texture. Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at…
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,…
We present a new type of three-dimensional essential Dirac semimetal with magnetic ordering. The Dirac points are protected by the magnetic space groups and cannot be gapped without lowering such symmetries, where the combined antiunitary…
We discuss the behaviour of the Dirac fermions in a general spherically symmetric black hole background with a non-trivial topology of the event horizon. Both massive and massless cases are taken into account. The analytical studies of…
Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general…
We present a systematic construction of non-Hermitian tight-binding lattices whose Bloch spectra are $n$th roots of those of Hermitian parent two-dimensional (2D) lattices, namely graphene and the Lieb lattice. The $n$-roots of these models…