Quantum Spin Hall Effect and Topologically Invariant Chern Numbers

Details Quantum Spin Hall Effect and Topologically Invariant Chern Numbers Quantum Spin Hall Effect and Topologically Invariant Chern Numbers

2006-03-02

arxiv.org/abs/cond-mat/0603054v1

Phys. Rev. Lett. 97, 036808 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages and 4 figures

Scientific paper

10.1103/PhysRevLett.97.036808

We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a $2\times 2$ traceless 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's 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.

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