Topological materials
Do topological edge states need a crystal lattice?
Open access · cc by · source: Europe PMC
Light-guiding one-way edge states, usually thought to need a periodic crystal, survived in a disordered (amorphous) lattice of magnetic rods but disappeared once the lattice lost its local order.
Study at a glance
- Design
- Other — Microwave parallel-plate waveguide experiments plus finite-element simulations on magnetically biased ferrite-rod lattices generated with disorder index 0, 0.1, 0.45 and 0.8.
- N
- No sample size; four fabricated lattices of different disorder, each measured for bulk and edge transmission and field maps.
- Population
- Two-dimensional lattices of yttrium iron garnet rods in a copper waveguide under a 0.2 T magnetic field
- Outcome
- Bulk transmission gap, forward/backward edge transmission, edge-field maps, Bott index, and nearest-neighbour coordination number
Structured fields used in claim comparison tables when every cited study has a complete layer.
Key findings
The crystal and the amorphous lattice with disorder index 0.1 both showed a bulk transmission gap (10.6 to 11.4 GHz for the amorphous sample) and strongly one-way edge transmission, and the amorphous lattice had a Bott index of 1 matching the crystal's Chern number. Edge waves travelled around a metal obstacle and through a cavity without backscattering. As disorder rose, the nearest-neighbour count fell from about 6 to about 2 with a sharp drop near disorder index 0.45; the topological window shrank there and edge states vanished entirely at 0.8.
Methodology
The authors generated rod arrangements by packing discs to different densities, from a perfect triangular crystal to glass-like and liquid-like layouts, and placed magnetised ferrite rods at those positions inside a microwave waveguide. They measured transmission through the bulk and along the edges in both directions, mapped the fields, and added obstacles or removed rods along the edge. They also computed a real-space topological invariant (the Bott index) and the average number of nearest neighbours to locate a glass transition.
Limitations
Only four lattices were fabricated, each 9 by 9 lattice constants, so the glass-transition point is located mainly by simulation and coordination-number trends. The experiment is at microwave frequencies with bulky magnetised ferrites, so it does not show that the effect works at optical frequencies or without strong magnetic bias. The authors note losses from imperfect contacts, drilled holes and material absorption, and the nature of the glass transition itself remains unexplained.
How this study connects
Role on claims
Each row is a claim on a concept or method page where this paper supports, challenges, or qualifies the statement. Roles are hand-checked — not a model guess.
Topology survives moderate disorder, but not unlimited disorder.
Protected edge transport does not need a crystal: a microwave lattice of magnetised ferrite rods kept a bulk gap, a Bott index of 1 and one-way edge waves that went around obstacles when mildly disordered (amorphous), but the topological window shrank near disorder index 0.45 and edge states vanished at 0.8.
Evidence for the claim as stated.
Measured versus predicted: the electronic and mechanical results (Bi2Se3 films, Mn(Bi,Sb)2Te4 Hall bars, truss lattices, ferrite rods, waveguides) come from fabricated samples, while the Weyl metamaterial, MnBi2Te4 optics and MoS2/CrBr3 flat Chern bands are theory or simulation with idealised, disorder-free structures.
Evidence for the claim as stated.
How robust is 'protected'? The amorphous photonic lattice and the SSH waveguide lattice both show protection failing once disorder or coupling closes the gap, which limits claims of unconditional robustness made in more idealised models.
Evidence for the claim as stated.
Open questions
Tensions this paper is part of
From concept pages' “where studies disagree.” Disagreement means the same question; scope means different assays, populations, or outcomes.
Measured versus predicted: the electronic and mechanical results (Bi2Se3 films, Mn(Bi,Sb)2Te4 Hall bars, truss lattices, ferrite rods, waveguides) come from fabricated samples, while the Weyl metamaterial, MnBi2Te4 optics and MoS2/CrBr3 flat Chern bands are theory or simulation with idealised, disorder-free structures.
- Supports · Can topological corner states survive inside the bulk energy band?
- Supports · Can swapping bismuth for antimony flip a magnet's Hall signals?
- Supports · Can a passive, static structure show one-way topological effects?
- Challenges · Can light bend the 'wrong' way at every angle with no reflection?
- Challenges · Can light absorption reveal the hidden geometry of electron waves?
- Challenges · Can magnetic skyrmions make flat topological bands?
How robust is 'protected'? The amorphous photonic lattice and the SSH waveguide lattice both show protection failing once disorder or coupling closes the gap, which limits claims of unconditional robustness made in more idealised models.
Related papers in this topic
Same topic cluster — not a recommendation engine.
- Can light's frequency act as an extra dimension for topology?
- Can topological insulators triple terahertz frequencies efficiently?
- Can topological corner states survive inside the bulk energy band?
- How do hot electrons change a Weyl semimetal's direction-dependence?
- Can a passive, static structure show one-way topological effects?