Tolerance and breakdown of topological protection in a disordered waveguide

TL;DR

This paper investigates how topological protection in a disordered waveguide is affected by different types of disorder, revealing conditions under which protection breaks down and localization occurs.

Contribution

It demonstrates the specific impact of radius disorder on topological protection and links disorder-induced localization to changes in the topological gap using the Bott index.

Findings

Protection is broken by radius disorder in the non-trivial lattice.

Donor and acceptor modes occupy the topological bandgap causing breakdown.

Anderson localization occurs with increasing disorder, changing the topological gap.

Abstract

We consider a disordered waveguide consisting of trivial dielectric and non-trivial magnetically anisotropic material. A topologically-protected edge mode appears owing to the broken time-reversal symmetry of the non-trivial lattice. While the edge mode maintains under other position and radius disorders, the protection is immediately broken by applying a radius disorder to the non-trivial lattice. This breakdown originates from donor and acceptor modes occupying the topological bandgap. Furthermore, via the calculation of the Bott index, we show that Anderson localization occurs as a metal conducting gap changes to a topological gap along with increasing disorders.