Related papers: Absolutely continuous spectrum for truncated topol…

Topological insulators are unique devices supporting unidirectional edge states at their interfaces. Due to topological protection, such edge states persist in the presence of disorder and do not experience backscattering upon interaction…

Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…

Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…

A theoretical investigation is made of acoustic wave propagation in a periodically stubbed waveguide. In general the waveguide segments and stubs are made of different materials. The acoustic wave in such a system has two independent…

The existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long range hopping in a…

We consider the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, studying the spectral theory of the Neumann--Poincar\'e operator of the boundary. A limiting absorption principle is proved, valid when the…

We study entanglement spectra of gapped states on the surfaces of symmetry-protected topological phases. These surface states carry anomalies that do not allow them to be terminated by a trivial state. Their entanglement spectra are…

A general partial-wave multiple scattering theory for scattering from cylindrically symmetric potentials on a topological insulator (TI) surface is developed. As an application, the cross sections for a single scatterer and two scatterers…

We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.

We deal with irregular curves contained in smooth, closed, and compact surfaces. For curves with finite total intrinsic curvature, a weak notion of parallel transport of tangent vector fields is well-defined in the Sobolev setting. Also,…

Topological insulators are most frequently constructed using lattices with specific degeneracies in their linear spectra, such as Dirac points. For a broad class of lattices, such as honeycomb ones, these points and associated Dirac cones…

A topological insulator possesses a bulk energy gap splitting the lowest empty band from the highest occupied electronic band. The electronic states at the surface (or edge in two dimensions), on the other hand, of a topological insulator…

Nontrivial properties of electronic states in topological insulators are inherent not only to the surface and boundary states, but to bound states localized at structure defects as well. We clarify how the unusual properties of the…

We introduce topological theory of perfect isolation: perfect transmission from one side and total reflection from another side simultaneously. The theory provides an efficient approach for determining whether such a perfect isolation point…

Twisted bilayer graphene gives rise to large moir\'{e} patterns that form a triangular network upon mechanical relaxation. If gating is included, each triangular region has gapped electronic Dirac points that behave as bulk topological…

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…

We show that there exist two dimensional (2D) time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a topological insulator can be fully gapped without breaking…

The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the…

We will consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random…

Fermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. These are characterized by a $\mathbb{Z}_2$-index: the Fu-Kane-Mele index. We prove that if two…