Related papers: Bulk-edge correspondence for unbounded Dirac-Landa…
In this article we develop a systematic approach to treat Dirac operators $A_{\eta, \tau, \lambda}$ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths $\eta, \tau, \lambda \in \mathbb{R}$,…
In this article, we study Schr\"odinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with the dislocation parameter. We introduce several…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…
For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface…
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the…
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From a mathematical point of view, their relationships are described by a certain 2-category associated to an even…
We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
We investigate the role of self-adjoint extensions in the bulk-edge correspondence for topological insulators. While the correspondence is well understood in discrete models with spectral gaps, complications arise in the presence of…
Consider electromagnetic waves in two-dimensional {\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\LA=-\nabla_\bx\cdot A(\bx)…
On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schr\"odinger operators. Assuming two Dirac-Schr\"odinger operators coincide at infinity, by previous…
We consider the two-dimensional Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a $C^4$-planar curve. Under generic assumptions on its curvature $\kappa$, we prove that in the thin-width regime the…
The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be…
We study the on-resonance Spin-1/2 Double Kicked Rotor, a periodically driven quantum system that hosts topological phases. Motivated by experimental constraints, we analyze the effects of open and periodic boundary conditions in contrast…
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…
The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. Unbounded perturbations of elliptic operators (in particular, integro-differential operators) are considered in plane bounded…
There are two types of edge states in graphene with/without magnetic field. One is a quantum Hall edge state, which is topologically protected against small perturbation. The other is a chiral zero mode that is localized near the boundary…
In [10], Dabrowski etc. gave spectral Einstein bilinear functionals of differential forms for the Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski…
For spin manifolds with boundary we consider Riemannian metrics which are product near the boundary and are such that the corresponding Dirac operator is invertible when half-infinite cylinders are attached at the boundary. The main result…