Quantum spin-hall effect and topologically invariant chern numbers

D. N. Sheng, Z. Y. Weng, L. Sheng, F. D.M. Haldane

Research output: Contribution to journalArticlepeer-review

506 Scopus citations


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 2×2 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 finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states and determine a phase diagram for the QSHE.

Original languageEnglish (US)
Article number036808
JournalPhysical review letters
Issue number3
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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