Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator

TL;DR

This paper investigates how vertex geometry influences topological bound states in a quasicrystalline topological insulator, revealing that structural changes can eliminate these states.

Contribution

It demonstrates through numerical simulations that vertex structure critically affects zero-dimensional topological states in a quasicrystalline insulator.

Findings

Vertex geometry significantly impacts bound state energies.

Alterations in vertex structure can cause bound states to vanish.

Zero-dimensional states are sensitive to topological and geometrical variations.

Abstract

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.