# 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
}
}
• Published 17 September 2018
• Physics, Medicine
• Physical review letters
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

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## References

SHOWING 1-10 OF 168 REFERENCES
Theory of spin Bott index for quantum spin Hall states in nonperiodic systems
• Physics
Physical 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
Quantum spin Hall phase in 2D trigonal lattice
• Physics, Medicine
Nature communications
• 2016
This exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement.
Quantum spin-Hall effect and topologically invariant Chern numbers.
• Physics, Medicine
Physical review letters
• 2006
It is shown that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers, and the nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM).
Formation of quantum spin Hall state on Si surface and energy gap scaling with strength of spin orbit coupling
• Physics, Medicine
Scientific reports
• 2014
This work demonstrates a unique approach to create the large-gap 2D TI state on a semiconductor surface, based on first-principles calculations and effective Hamiltonian analysis, and finds that within this model, the SOC gap does not increase monotonically with the increasing strength of SOC.
Z2 topological order and the quantum spin Hall effect.
• Physics, Medicine
Physical review letters
• 2005
The Z2 order of the QSH phase is established in the two band model of graphene and a generalization of the formalism applicable to multiband and interacting systems is proposed.
Large-Gap Quantum Spin Hall State in MXenes: d-Band Topological Order in a Triangular Lattice.
• Materials Science, Medicine
Nano letters
• 2016
It is predicted that Mo2MC2O2 (M = Ti, Zr, or Hf), belonging to a recently discovered new class of MXenes with double transition metal elements in an ordered structure, are robust quantum spin Hall (QSH) insulators.
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Physics, Medicine
Science
• 2006
We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride
Topological states of non-Dirac electrons on a triangular lattice
• Physics
• 2016
We demonstrate the possibility of topological states for non-Dirac electrons. Specifically it is shown that, because of the $C_{\rm 3}$ crystal symmetry and time reversal symmetry, $p_x$ and $p_y$
Quantum Spin Hall Insulator State in HgTe Quantum Wells
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.
Quantum spin Hall effect.
• Physics, Medicine
Physical review letters
• 2006
This work predicts a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi).