# Amorphous topological insulators constructed from random point sets

@article{Mitchell2016AmorphousTI, title={Amorphous topological insulators constructed from random point sets}, author={Noah P. Mitchell and Lisa M. Nash and Daniel Hexner and Ari M. Turner and William T. M. Irvine}, journal={Nature Physics}, year={2016}, volume={14}, pages={380-385} }

The discovery that the band structure of electronic insulators may be topologically non-trivial has revealed distinct phases of electronic matter with novel properties1,2. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations3,4, giving rise to protected unidirectional edge modes5–7. In all of these cases, however, as well as in other topological metamaterials3,8, the underlying structure was finely tuned, be it through periodicity, quasi…

## 161 Citations

### Topological Insulators Constructed from Random Point Sets

- Physics
- 2020

The discovery that the band structure of electronic insulators may be topologically non-trivial has revealed distinct phases of electronic matter with novel properties. Recently, mechanical lattices…

### Amorphous topological superconductivity in a Shiba glass

- PhysicsNature Communications
- 2018

It is shown that subgap Yu–Shiba–Rusinov states on the magnetic moments form a topological superconducting phase at critical density despite a complete absence of spatial order, demonstrating the physical feasibility of amorphous topological quantum matter.

### Photonic amorphous topological insulator

- PhysicsLight, science & applications
- 2020

By tuning the disorder strength in the lattice, it is demonstrated that photonic topological edge states can persist into the amorphous regime prior to the glass-to-liquid transition, paving the way for new classes of non-crystalline topological photonic bandgap materials.

### Towards Realistic Amorphous Topological Insulators.

- PhysicsNano letters
- 2019

This study presents a realistic state-of-the-art study of the electronic and transport properties of amorphous bismuthene systems, showing that these materials are topological insulators.

### Fractionalization and topology in amorphous electronic solids

- Physics
- 2022

Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological…

### Structural Amorphization-Induced Topological Order.

- Physics, Materials SciencePhysical review letters
- 2022

Electronic properties of crystals are inherently pertained to crystalline symmetry, so that amorphization that lowers and breaks symmetry is detrimental. One important crystalline property is…

### Symmetry-Protected Topological Phases in a Rydberg Glass.

- Physics, Materials SciencePhysical review letters
- 2021

This work finds symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies.

### Topological Weaire–Thorpe models of amorphous matter

- Materials ScienceProceedings of the National Academy of Sciences
- 2020

The topological Weaire–Thorpe class of models are introduced, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amoralous solids and allow us to analytically predict spectral gaps in topological systems.

### Topological and conventional phases of a three-dimensional electronic glass

- Physics, Materials SciencePhysical Review B
- 2020

We investigate a symmetry protected $Z_2$ topological electron glass -- a glassy equivalent of the $Z_2$ topological band insulator in crystalline systems -- and uncover associated quantum phase…

### Topological valley transport under long-range deformations

- Materials SciencePhysical Review Research
- 2020

Edge states protected by bulk topology of photonic crystals show robustness against short-range disorder, making robust information transfer possible. Here, topological photonic crystals under…

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