Quantum spin-Hall effect and topologically invariant Chern numbers.

@article{Sheng2006QuantumSE,
  title={Quantum spin-Hall effect and topologically invariant Chern numbers.},
  author={Donna N. Sheng and Zheng-yu Weng and Li Sheng and F. D. M. Haldane},
  journal={Physical review letters},
  year={2006},
  volume={97 3},
  pages={
          036808
        }
}
We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of… Expand
View on PubMed
scholarworks.csun.edu
333 Citations
Highly Influential Citations
2
Background Citations
49
Methods Citations
18
Results Citations
1

333 Citations

Citation Type

Citation Type

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems
For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance and time-reversal symmetry breaking… Expand
Quantum anomalous Hall-quantum spin Hall effect in optical superlattices.
TLDR
A new category of gap-dependent QAH--QSH insulator paves the way for the possible observation of the coexistence of QSH and QAH effects at one platform. Expand
The topological quantum phase transitions in Lieb lattice driven by the Rashba SOC and exchange field
Abstract The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange… Expand
An edge index for the quantum spin-Hall effect
Quantum spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the quantum Hall systems where the charge… Expand
Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect
The quantum spin Hall (QSH) effect is considered to be unstable to perturbations violating the time-reversal (TR) symmetry. We review some recent developments in the search of the QSH effect in the… Expand
Chern number matrix of non-Abelian spin-singlet fractional quantum Hall effect
  • Tian-Sheng Zeng, W. Zhu
  • Physics
  • 2021
While the understanding of Abelian topological order is comprehensive, how to describe the internal correlation structure of non-Abelian states is still outstanding. Here, we propose a general scheme… Expand
TOPOLOGICAL QUANTUM PHASE TRANSITION BETWEEN QUANTUM SPIN HALL STATE AND QUANTUM ANOMALOUS HALL STATE
In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous… Expand
Mapping Chern numbers in quasi-periodic interacting spin chains.
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… Expand
Spin Chern number and topological phase transition on the Lieb lattice with spin–orbit coupling
Abstract We propose that quantum anomalous Hall effect may occur in the Lieb lattice, when Rashba spin–orbit coupling, spin-independent and spin-dependent staggered potentials are introduced into the… Expand
Time-reversal-breaking induced quantum spin Hall effect
TLDR
It is shown that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths, but it can be induced by the presence of staggered magnetic fluxes alternating directions square by square. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 50 REFERENCES
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.
TLDR
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). Expand
Nondissipative spin Hall effect via quantized edge transport.
TLDR
The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically and it is shown that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system. Expand
Stability of the quantum spin Hall effect: Effects of interactions, disorder, and Z 2 topology
The stability to interactions and disorder of the quantum spin Hall effect (QSHE) proposed for time-reversal-invariant 2D systems is discussed. The QSHE requires an energy gap in the bulk and gapless… Expand
Helical liquid and the edge of quantum spin Hall systems.
TLDR
A no-go theorem is proved which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. Expand
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
Spin Hall effect and spin transfer in a disordered Rashba model
Based on numerical study of the Rashba model, we show that the spin Hall conductance remains finite in the presence of disorder up to a characteristic length scale, beyond which it vanishes… Expand
Universal intrinsic spin Hall effect.
TLDR
It is argued that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic, and the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening. Expand
Phase diagram for quantum hall bilayers at nu=1.
TLDR
Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally. Expand
Quantized Hall conductance as a topological invariant.
TLDR
The new formulation generalizes the earlier result and draws the conclusion that there must be a symmetry breaking in the many-body ground state when applying to the fractional quantized Hall effect. Expand
...
1
2
3
4
5
...