# Topologically Localized Insulators.

@article{Lapierre2021TopologicallyLI, title={Topologically Localized Insulators.}, author={Bastien Lapierre and Titus Neupert and Luka Trifunovic}, journal={Physical review letters}, year={2021}, volume={129 25}, pages={ 256401 } }

We show that fully localized, three-dimensional, time-reversal-symmetry-broken insulators do not belong to a single phase of matter but can realize topologically distinct phases that are labeled by integers. The phase transition occurs only when the system becomes conducting at some filling. We find that these novel topological phases are fundamentally distinct from insulators without disorder: they are guaranteed to host delocalized boundary states giving rise to the quantized boundary Hall…

## References

SHOWING 1-10 OF 24 REFERENCES

### Periodic table for topological insulators and superconductors

- Physics, Mathematics
- 2009

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a…

### Higher-order topological insulators

- PhysicsScience Advances
- 2018

The notion of three-dimensional topological insulators is extended to systems that host no gapless surface states but exhibit topologically protected gapless hinge states and it is shown that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topology insulators.

### Observation of a large-gap topological-insulator class with a single Dirac cone on the surface

- Physics
- 2009

Recent experiments and theories have suggested that strong spin–orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator,…

### Topological insulators and superconductors: tenfold way and dimensional hierarchy

- Physics
- 2009

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological…

### Disordered topological insulators: a non-commutative geometry perspective

- Physics
- 2011

The progress in the field of topological insulators is impetuous, being sustained by a suite of exciting results on three fronts: experiment, theory and numerical simulation. Very often, the…

### Spontaneously polarized half-gapped superconductivity

- Physics
- 2018

Nonunitary superconductivity is a rare and striking phenomenon in which spin up and spin down electrons segregate into two different quantum condensates. Because they support topological excitations,…

### Topological quantum chemistry

- PhysicsNature
- 2017

A complete electronic band theory is proposed, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding and can be used to predict many more topological insulators.

### Percolation, quantum tunnelling and the integer Hall effect

- Physics
- 1988

A model is introduced for Anderson localisation in the integer quantum Hall regime. The model represents a system with a disordered potential that varies slowly on the scale of the magnetic length,…

### Symmetry-based indicators of band topology in the 230 space groups

- PhysicsNature Communications
- 2017

The authors present a framework for identifying topologically distinct band-structures for all 3D space groups by developing an efficient way to represent band structures in terms of elementary basis states, and isolating the topological ones by removing the subset of atomic insulators.

### Quantum Spin Hall Insulator State in HgTe Quantum Wells

- PhysicsScience
- 2007

The quantum phase transition at the critical thickness, d = 6.3 nanometers, was independently determined from the magnetic field–induced insulator-to-metal transition, providing experimental evidence of the quantum spin Hall effect.