Topologically non-trivial quantum layers
نویسنده
چکیده
Given a complete non-compact surface Σ embedded in R, we consider the Dirichlet Laplacian in the layer Ω that is defined as a tubular neighbourhood of constant width about Σ. Using an intrinsic approach to the geometry of Ω, we generalise the spectral results of the original paper [1] by Duclos et al. to the situation when Σ does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain Ω.
منابع مشابه
اثر برهمکنش اسپین مدار یکنواخت و میدان مغناطیسی یکنواخت بر خواص توپولوژیکی یک نانو سیم یک بعدی کوانتومی
We theoretically demonstrate the interplay of uniform spin-orbit coupling and uniform Zeeman magnetic field on the topological properties of one-dimensional double well nano wire which is known as Su-Schrieffer-Heeger (SSH) model. The system in the absence of Zeeman magnetic field and presence of uniform spin-orbit coupling exhibits topologically trivial/non–trivial insulator depending on the h...
متن کاملTopologically protected surface states in non-centrosymmetric superconductors
The hallmark of topological insulators and superconductors is the existence of topologically protected zeroenergy surface or edge states, some of which are of Majorana type. The experimental observation of these edge and surface states in HgTe/(Hg,Ce)Te quantum wells and in BiSb alloys, respectively, has lead to a renewed interest in topological states of matter. Recently, we have shown that to...
متن کاملCorrelation between topological band character and chemical bonding in a Bi14Rh3I9-based family of insulators
Recently the presence of topologically protected edge-states in Bi14Rh3I9 was confirmed by scanning tunnelling microscopy consolidating this compound as a weak 3D topological insulator (TI). Here, we present a density-functional-theory-based study on a family of TIs derived from the Bi14Rh3I9 parent structure via substitution of Ru, Pd, Os, Ir and Pt for Rh. Comparative analysis of the band-str...
متن کاملUniform semiclassical approximations on a topologically non-trivial configuration space The hydrogen atom in an electric field
Semiclassical periodic-orbit theory and closed-orbit theory represent a quantum spectrum as a superposition of contributions from individual classical orbits. Close to a bifurcation, these contributions diverge and have to be replaced with a uniform approximation. Its construction requires a normal form that provides a local description of the bifurcation scenario. Usually, the normal form is c...
متن کاملTopological glass states
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local bonding enforces constraints on low energy states which organize themselves into topologically distinct classes that break ergodicity but not any apparent symm...
متن کامل