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

@article{Huang2018TheoryOS,
  title={Theory of spin Bott index for quantum spin Hall states in nonperiodic systems},
  author={Huaqing Huang and Feng Liu},
  journal={Physical Review B},
  year={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 index to characterize the electronic topology in aperiodic and amorphous systems, and confirm its applicability by realizing the QSHE in quasicrystals. As in crystals, the QSHE in quasicrystals manifests with robust metallic edge states and quantized conductance. Their findings not only provide a better… Expand
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References

SHOWING 1-10 OF 131 REFERENCES
Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice.
TLDR
This work proposes that the QSH effect can be realized in quasicrystal lattices (QLs), and shows that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index B_{s}. Expand
Z2 topological order and the quantum spin Hall effect.
TLDR
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. Expand
Quantum spin-Hall effect and topologically invariant Chern numbers.
TLDR
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). Expand
Quantum Spin Hall Effect in Three Dimensional Materials : Lattice Computation of Z_2 Topological Invariants and Its Application to Bi and Sb(Condensed matter: electronic structure and electrical, magnetic, and optical properties)
We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numericalExpand
Quantum spin Hall effect in graphene.
TLDR
Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed. Expand
Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb
We derive an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numericalExpand
Scattering formula for the topological quantum number of a disordered multimode wire
The topological quantum number Q of a superconducting or chiral insulating wire counts the number of stable bound states at the end points. We determine Q from the matrix r of reflection amplitudesExpand
Theory of the topological anderson insulator.
TLDR
An effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells, and the mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling. Expand
Topological aspects of the quantum spin-Hall effect in graphene: Z2 topological order and spin Chern number
For generic time-reversal-invariant systems with spin-orbit couplings, we clarify a close relationship between the ${\mathrm{Z}}_{2}$ topological order and the spin Chern number (SChN) in the quantumExpand
Periodic table for topological insulators and superconductors
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 aExpand
...
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3
4
5
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