English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present the {\em (symmetry-incorporating) formalism of general continuummodels with boundary conditions} and apply it to the model with the minimalnumber of degrees of freedom necessary to have a well-defined boundary: a modelwith a two-component wave function and a linear-in-momentum Hamiltonian. Wederive the most general forms (class A) of both the Hamiltonian and boundarycondition in 1D (insulator), 2D (quantum anomalous Hall insulator), and 3D(Weyl node) and analytically calculate and explore the corresponding generalbound/edge/surface-state structures. In 1D, one bound state exists in the halfof the $\text{U}(1)$ parameter space of possible boundary conditions.Considering several dimensions simultaneously ties the models together anduncovers important relations between them. We formulate a version ofbulk-boundary correspondence that fully characterizes the vicinity of a Weylpoint: the chirality of the surface-state spectrum along a path enclosing theprojected Weyl point is equal to the Chern number of the Weyl point. Wedemonstrate how symmetries are naturally incorporated into the formalism, byderiving the most general form of the model with chiral symmetry (class AIII).We show that the (perhaps unexpected) existence of persistent bound states inthe topologically trivial 1D class-A model is not accidental and has at leasttwo topological explanations, by relating it to the topologically nontrivial 2Dclass-A (by viewing it as an effective 2D quantum anomalous Hall system) and 1Dclass-AIII (via deviation from the cases of chiral symmetry in the parameterspace) models. We identify this as a systematic "propagation effect", wherebybound states from topologically nontrivial classes, where they are protectedand guaranteed to exist, propagate to the related, "adjacent" in dimension orsymmetry, topologically trivial classes.

Formalism of general continuum models with boundary conditions,  propagation of bound states from nontrivial to trivial topological classes,  and the general surface-state structure near one node of a Weyl semimetal