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… 

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References

SHOWING 1-10 OF 29 REFERENCES

Topological Insulators in Amorphous Systems.

TLDR
This study provides a novel theoretical demonstration of realizing topological phases in amorphous systems, as exemplified by a set of sites randomly located in space, by constructing hopping models on such random lattices whose gapped ground states are shown to possess nontrivial topological nature.

Photonic Floquet topological insulators

TLDR
This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.

Observation of phononic helical edge states in a mechanical topological insulator

TLDR
The collective behavior of mechanical oscillators exhibiting the phenomenology of the quantum spin Hall effect is characterized, and the phononic edge modes are shown to be helical, and this may enable the design of topological acoustic metamaterials that can capitalize on the stability of the surface phonons as reliable wave guides.

Experimental realization of the topological Haldane model with ultracold fermions

TLDR
The experimental realization of the Haldane model and the characterization of its topological band structure are reported, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice and a direct extension to realize spin-dependent topological Hamiltonians is proposed.

Geared topological metamaterials with tunable mechanical stability

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics,

Mapping topological order in coordinate space

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wave function. Here we address the Chern number of a

Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice

TLDR
The concept of topological order in classical acoustics is introduced, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice biased with angular momentum, forming the acoustic analogue of a magnetically biased graphene layer.

Electronic properties of an amorphous solid. II. Further aspects of the theory

A further study is made of the properties of the simple tight-binding Hamiltonian for which Weaire has recently shown that a band gap exists in a tetrahedrally bonded solid regardless of its

Topological Phononic Crystals with One-Way Elastic Edge Waves.

TLDR
A new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves, which could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Topological insulators in three dimensions.

TLDR
A tight binding model is introduced which realizes the WTI and STI phases, and its relevance to real materials, including bismuth is discussed.