# Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice.

@article{Huang2018QuantumSH, title={Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice.}, author={Huaqing Huang and Feng Liu}, journal={Physical review letters}, year={2018}, volume={121 12}, pages={ 126401 } }

Despite the rapid progress in the field of the quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index B_{s}. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index B_{s}=1, associated with robust edge states and quantized…

## 59 Citations

Theory of spin Bott index for quantum spin Hall states in nonperiodic systems

- PhysicsPhysical Review B
- 2018

Quantum spin Hall effects (QSHE) arising from electron band topology are usually limited to crystals. Here, the authors extend the concept of QSHE to nonperiodic systems. They derive a spin Bott…

Comparison of quantum spin Hall states in quasicrystals and crystals

- PhysicsPhysical Review B
- 2019

We theoretically study the quantum spin Hall states in an Ammann-Beenker-type octagonal quasicrystal and a periodic snub-square crystal, both sharing the same basic building blocks. Although the bulk…

Topological Anderson insulator phase in a quasicrystal lattice

- PhysicsPhysical Review B
- 2019

Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on…

Higher-Order Topological Insulators in Quasicrystals.

- Medicine, PhysicsPhysical review letters
- 2020

This work shows that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns, and reveals some unusual features of the corner states (CSs) in the quAsicRYstalline SOTIs.

Engineering a topological quantum dot device through planar magnetization in bismuthene

- PhysicsPhysical Review B
- 2019

The discovery of quantum spin Hall materials with huge bulk gaps in experiment, such as bismuthene, provides a versatile platform for topological devices. We propose a topological quantum dot (QD)…

Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis

- Physics
- 2020

Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and…

Quasicrystalline Chern insulators

- Physics
- 2019

Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices…

A Unified View of Topological Phase Transition in Band Theory

- Medicine, Materials ScienceResearch
- 2020

It is demonstrated that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory.

Aperiodic topological crystalline insulators

- Physics, Materials Science
- 2020

Topological crystalline insulators (TCIs) are usually described with topological protection imposed by the crystalline symmetry. In general, however, the existence of TCI states does not necessitate…

Mapping Chern numbers in quasi-periodic interacting spin chains.

- Physics
- 2020

Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary…

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