Do topological edge states need a crystal lattice?
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.
Source
Photonic amorphous topological insulator
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.
What they did
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.
What they found
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.
The limits
What it doesn't show
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.
Key terms
- Photonic topological insulator
- A photonic material with a bandgap whose band topology guarantees edge states that resist scattering.
- Chern number / Bott index
- Integer topological invariants; the Chern number needs a periodic band structure, while the Bott index can be computed in real space for non-periodic lattices.
- Amorphous lattice
- An arrangement with short-range order (regular local neighbours) but no long-range periodicity, like glass.
- Pair correlation function g(r)
- The relative probability of finding another site at distance r; sharp peaks mean order, g(r) ≈ 1 means randomness.
- Coordination number
- The average number of nearest neighbours around each site; about 6 for this crystal, about 2 for the liquid-like case.
Flashcards
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Quiz yourself
What distinguishes an amorphous lattice from a crystal?
Common questions
How can a lattice without periodicity be topological?
Topology can be defined in real space with the Bott index, and what matters is short-range connectivity rather than long-range periodicity.
Why does the magnetic field matter?
It biases the gyromagnetic rods to break time-reversal symmetry, which is needed for one-way Chern-type edge states.
What kills the edge states at high disorder?
Loss of short-range order through the glass transition closes the bulk mobility gap, removing topological protection.
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