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… 
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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.
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).
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.
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…
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.
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.
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…
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.
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.
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.
...
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2
3
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